https://github.com/BaseMax/MatrixResearch/blob/master/result.md
f(x, y) = ax + by + cxy + d
f(x, y) = ax^2 + bx + cy^2 + dy + exy + f
[matrix's width] x [matrix's height] => [count of submatrix(s)] , [count of answer of first formula] , [count of answer of second formula]
1 x 1 => 1 , 6160 , 2243934
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1 x 2 => 3 , 3810 , 1553244
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1 x 3 => 6 , 2673 , 1126493
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1 x 4 => 10 , 2009 , 866046
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1 x 5 => 15 , 1600 , 691166
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1 x 6 => 21 , 1260 , 565516
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1 x 7 => 28 , 1071 , 472199
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1 x 8 => 36 , 891 , 400983
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1 x 9 => 45 , 816 , 345904
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1 x 10 => 55 , 682 , 301444
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1 x 11 => 66 , 615 , 265215
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1 x 12 => 78 , 522 , 234900
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1 x 13 => 91 , 518 , 209958
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1 x 14 => 105 , 378 , 186732
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1 x 15 => 120 , 429 , 169325
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1 x 16 => 136 , 325 , 151475
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1 x 17 => 153 , 348 , 137628
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1 x 18 => 171 , 276 , 124200
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1 x 19 => 190 , 275 , 112651
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1 x 20 => 210 , 231 , 102102
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2 x 1 => 3 , 3810 , 828574
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2 x 2 => 9 , 2135 , 673932
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2 x 3 => 18 , 1520 , 568988
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2 x 4 => 30 , 1198 , 473732
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2 x 5 => 45 , 910 , 363026
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2 x 6 => 63 , 703 , 285805
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2 x 7 => 84 , 608 , 251090
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2 x 8 => 108 , 522 , 219086
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2 x 9 => 135 , 404 , 175085
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2 x 10 => 165 , 315 , 138400
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2 x 11 => 198 , 277 , 119536
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2 x 12 => 234 , 228 , 102312
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2 x 13 => 273 , 184 , 78368
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2 x 14 => 315 , 135 , 59535
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2 x 15 => 360 , 108 , 48778
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2 x 16 => 408 , 90 , 38040
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2 x 17 => 459 , 57 , 25628
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2 x 18 => 513 , 36 , 15645
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2 x 19 => 570 , 17 , 8886
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2 x 20 => 630 , 1 , 3609
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3 x 1 => 6 , 2673 , 400083
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3 x 2 => 18 , 1520 , 362473
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3 x 3 => 36 , 1023 , 315315
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3 x 4 => 60 , 771 , 261302
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3 x 5 => 90 , 609 , 211211
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3 x 6 => 126 , 479 , 171298
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3 x 7 => 168 , 376 , 138383
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3 x 8 => 216 , 275 , 109533
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3 x 9 => 270 , 196 , 83629
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3 x 10 => 330 , 135 , 60360
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3 x 11 => 396 , 82 , 40176
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3 x 12 => 468 , 37 , 23947
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3 x 13 => 546 , 6 , 12280
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3 x 14 => 630 , 0 , 5040
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3 x 15 => 720 , 0 , 1372
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3 x 16 => 816 , 0 , 127
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3 x 17 => 918 , 0 , 0
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3 x 18 => 1026 , 0 , 0
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3 x 19 => 1140 , 0 , 0
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3 x 20 => 1260 , 0 , 0
-----------
4 x 1 => 10 , 2009 , 232332
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4 x 2 => 30 , 1198 , 227272
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4 x 3 => 60 , 771 , 195133
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4 x 4 => 100 , 541 , 158300
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4 x 5 => 150 , 434 , 133516
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4 x 6 => 210 , 330 , 109195
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4 x 7 => 280 , 198 , 78801
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4 x 8 => 360 , 100 , 53743
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4 x 9 => 450 , 33 , 36583
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4 x 10 => 550 , 1 , 22159
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4 x 11 => 660 , 0 , 9923
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4 x 12 => 780 , 0 , 3153
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4 x 13 => 910 , 0 , 587
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4 x 14 => 1050 , 0 , 12
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4 x 15 => 1200 , 0 , 0
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4 x 16 => 1360 , 0 , 0
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4 x 17 => 1530 , 0 , 0
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4 x 18 => 1710 , 0 , 0
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4 x 19 => 1900 , 0 , 0
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4 x 20 => 2100 , 0 , 0
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5 x 1 => 15 , 1600 , 153288
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5 x 2 => 45 , 910 , 143836
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5 x 3 => 90 , 609 , 130868
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5 x 4 => 150 , 434 , 113989
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5 x 5 => 225 , 350 , 109062
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5 x 6 => 315 , 153 , 68676
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5 x 7 => 420 , 47 , 48187
-----------
5 x 8 => 540 , 1 , 31234
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5 x 9 => 675 , 0 , 17889
-----------
5 x 10 => 825 , 0 , 9693
-----------
5 x 11 => 990 , 0 , 2413
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5 x 12 => 1170 , 0 , 260
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5 x 13 => 1365 , 0 , 0
-----------
5 x 14 => 1575 , 0 , 0
-----------
5 x 15 => 1800 , 0 , 0
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5 x 16 => 2040 , 0 , 0
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5 x 17 => 2295 , 0 , 0
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5 x 18 => 2565 , 0 , 0
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5 x 19 => 2850 , 0 , 0
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5 x 20 => 3150 , 0 , 0
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6 x 1 => 21 , 1260 , 104160
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6 x 2 => 63 , 703 , 96061
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6 x 3 => 126 , 479 , 91707
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6 x 4 => 210 , 330 , 85134
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6 x 5 => 315 , 153 , 64596
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6 x 6 => 441 , 36 , 54750
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6 x 7 => 588 , 0 , 32427
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6 x 8 => 756 , 0 , 19983
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6 x 9 => 945 , 0 , 9775
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6 x 10 => 1155 , 0 , 3281
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6 x 11 => 1386 , 0 , 492
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6 x 12 => 1638 , 0 , 0
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6 x 13 => 1911 , 0 , 0
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6 x 14 => 2205 , 0 , 0
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6 x 15 => 2520 , 0 , 0
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6 x 16 => 2856 , 0 , 0
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6 x 17 => 3213 , 0 , 0
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6 x 18 => 3591 , 0 , 0
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6 x 19 => 3990 , 0 , 0
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6 x 20 => 4410 , 0 , 0
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7 x 1 => 28 , 1071 , 79065
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7 x 2 => 84 , 608 , 75021
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7 x 3 => 168 , 376 , 68931
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7 x 4 => 280 , 198 , 60443
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7 x 5 => 420 , 47 , 49321
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7 x 6 => 588 , 0 , 35784
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7 x 7 => 784 , 0 , 22815
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7 x 8 => 1008 , 0 , 12897
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7 x 9 => 1260 , 0 , 5799
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7 x 10 => 1540 , 0 , 1509
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7 x 11 => 1848 , 0 , 51
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7 x 12 => 2184 , 0 , 0
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7 x 13 => 2548 , 0 , 0
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7 x 14 => 2940 , 0 , 0
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7 x 15 => 3360 , 0 , 0
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7 x 16 => 3808 , 0 , 0
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7 x 17 => 4284 , 0 , 0
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7 x 18 => 4788 , 0 , 0
-----------
7 x 19 => 5320 , 0 , 0
-----------
7 x 20 => 5880 , 0 , 0
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8 x 1 => 36 , 891 , 58736
-----------
8 x 2 => 108 , 522 , 60984
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8 x 3 => 216 , 275 , 53140
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8 x 4 => 360 , 100 , 44928
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8 x 5 => 540 , 1 , 38741
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8 x 6 => 756 , 0 , 29367
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8 x 7 => 1008 , 0 , 17919
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8 x 8 => 1296 , 0 , 10575
-----------
8 x 9 => 1620 , 0 , 3605
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8 x 10 => 1980 , 0 , 695
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8 x 11 => 2376 , 0 , 0
-----------
8 x 12 => 2808 , 0 , 0
-----------
8 x 13 => 3276 , 0 , 0
-----------
8 x 14 => 3780 , 0 , 0
-----------
8 x 15 => 4320 , 0 , 0
-----------
8 x 16 => 4896 , 0 , 0
-----------
8 x 17 => 5508 , 0 , 0
-----------
8 x 18 => 6156 , 0 , 0
-----------
8 x 19 => 6840 , 0 , 0
-----------
8 x 20 => 7560 , 0 , 0
-----------
9 x 1 => 45 , 816 , 49422
-----------
9 x 2 => 135 , 404 , 45829
-----------
9 x 3 => 270 , 196 , 42336
-----------
9 x 4 => 450 , 33 , 37069
-----------
9 x 5 => 675 , 0 , 30376
-----------
9 x 6 => 945 , 0 , 22372
-----------
9 x 7 => 1260 , 0 , 13678
-----------
9 x 8 => 1620 , 0 , 7241
-----------
9 x 9 => 2025 , 0 , 3243
-----------
9 x 10 => 2475 , 0 , 268
-----------
9 x 11 => 2970 , 0 , 0
-----------
9 x 12 => 3510 , 0 , 0
-----------
9 x 13 => 4095 , 0 , 0
-----------
9 x 14 => 4725 , 0 , 0
-----------
9 x 15 => 5400 , 0 , 0
-----------
9 x 16 => 6120 , 0 , 0
-----------
9 x 17 => 6885 , 0 , 0
-----------
9 x 18 => 7695 , 0 , 0
-----------
9 x 19 => 8550 , 0 , 0
-----------
9 x 20 => 9450 , 0 , 0
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10 x 1 => 55 , 682 , 39116
-----------
10 x 2 => 165 , 315 , 35574
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10 x 3 => 330 , 135 , 35090
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10 x 4 => 550 , 1 , 32240
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10 x 5 => 825 , 0 , 29187
-----------
10 x 6 => 1155 , 0 , 17529
-----------
10 x 7 => 1540 , 0 , 11350
-----------
10 x 8 => 1980 , 0 , 5685
-----------
10 x 9 => 2475 , 0 , 1699
-----------
10 x 10 => 3025 , 0 , 88
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10 x 11 => 3630 , 0 , 0
-----------
10 x 12 => 4290 , 0 , 0
-----------
10 x 13 => 5005 , 0 , 0
-----------
10 x 14 => 5775 , 0 , 0
-----------
10 x 15 => 6600 , 0 , 0
-----------
10 x 16 => 7480 , 0 , 0
-----------
10 x 17 => 8415 , 0 , 0
-----------
10 x 18 => 9405 , 0 , 0
-----------
10 x 19 => 10450 , 0 , 0
-----------
10 x 20 => 11550 , 0 , 0
-----------
11 x 1 => 66 , 615 , 33210
-----------
11 x 2 => 198 , 277 , 31631
-----------
11 x 3 => 396 , 82 , 29150
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11 x 4 => 660 , 0 , 25495
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11 x 5 => 990 , 0 , 21080
-----------
11 x 6 => 1386 , 0 , 15696
-----------
11 x 7 => 1848 , 0 , 9473
-----------
11 x 8 => 2376 , 0 , 4378
-----------
11 x 9 => 2970 , 0 , 1234
-----------
11 x 10 => 3630 , 0 , 23
-----------
11 x 11 => 4356 , 0 , 0
-----------
11 x 12 => 5148 , 0 , 0
-----------
11 x 13 => 6006 , 0 , 0
-----------
11 x 14 => 6930 , 0 , 0
-----------
11 x 15 => 7920 , 0 , 0
-----------
11 x 16 => 8976 , 0 , 0
-----------
11 x 17 => 10098 , 0 , 0
-----------
11 x 18 => 11286 , 0 , 0
-----------
11 x 19 => 12540 , 0 , 0
-----------
11 x 20 => 13860 , 0 , 0
-----------
12 x 1 => 78 , 522 , 26316
-----------
12 x 2 => 234 , 228 , 26608
-----------
12 x 3 => 468 , 37 , 24144
-----------
12 x 4 => 780 , 0 , 20055
-----------
12 x 5 => 1170 , 0 , 17934
-----------
12 x 6 => 1638 , 0 , 11310
-----------
12 x 7 => 2184 , 0 , 7945
-----------
12 x 8 => 2808 , 0 , 3331
-----------
12 x 9 => 3510 , 0 , 857
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12 x 10 => 4290 , 0 , 4
-----------
12 x 11 => 5148 , 0 , 0
-----------
12 x 12 => 6084 , 0 , 0
-----------
12 x 13 => 7098 , 0 , 0
-----------
12 x 14 => 8190 , 0 , 0
-----------
12 x 15 => 9360 , 0 , 0
-----------
12 x 16 => 10608 , 0 , 0
-----------
12 x 17 => 11934 , 0 , 0
-----------
12 x 18 => 13338 , 0 , 0
-----------
12 x 19 => 14820 , 0 , 0
-----------
12 x 20 => 16380 , 0 , 0
-----------
13 x 1 => 91 , 518 , 24124
-----------
13 x 2 => 273 , 184 , 22648
-----------
13 x 3 => 546 , 6 , 19830
-----------
13 x 4 => 910 , 0 , 17690
-----------
13 x 5 => 1365 , 0 , 14463
-----------
13 x 6 => 1911 , 0 , 11550
-----------
13 x 7 => 2548 , 0 , 7020
-----------
13 x 8 => 3276 , 0 , 2823
-----------
13 x 9 => 4095 , 0 , 625
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13 x 10 => 5005 , 0 , 0
-----------
13 x 11 => 6006 , 0 , 0
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13 x 12 => 7098 , 0 , 0
-----------
13 x 13 => 8281 , 0 , 0
-----------
13 x 14 => 9555 , 0 , 0
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13 x 15 => 10920 , 0 , 0
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13 x 16 => 12376 , 0 , 0
-----------
13 x 17 => 13923 , 0 , 0
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13 x 18 => 15561 , 0 , 0
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13 x 19 => 17290 , 0 , 0
-----------
13 x 20 => 19110 , 0 , 0
-----------
14 x 1 => 105 , 378 , 16324
-----------
14 x 2 => 315 , 135 , 18360
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14 x 3 => 630 , 0 , 17207
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14 x 4 => 1050 , 0 , 16380
-----------
14 x 5 => 1575 , 0 , 13307
-----------
14 x 6 => 2205 , 0 , 9180
-----------
14 x 7 => 2940 , 0 , 5826
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14 x 8 => 3780 , 0 , 2579
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14 x 9 => 4725 , 0 , 498
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14 x 10 => 5775 , 0 , 0
-----------
14 x 11 => 6930 , 0 , 0
-----------
14 x 12 => 8190 , 0 , 0
-----------
14 x 13 => 9555 , 0 , 0
-----------
14 x 14 => 11025 , 0 , 0
-----------
14 x 15 => 12600 , 0 , 0
-----------
14 x 16 => 14280 , 0 , 0
-----------
14 x 17 => 16065 , 0 , 0
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14 x 18 => 17955 , 0 , 0
-----------
14 x 19 => 19950 , 0 , 0
-----------
14 x 20 => 22050 , 0 , 0
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15 x 1 => 120 , 429 , 18249
-----------
15 x 2 => 360 , 108 , 16899
-----------
15 x 3 => 720 , 0 , 15082
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15 x 4 => 1200 , 0 , 14194
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15 x 5 => 1800 , 0 , 13195
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15 x 6 => 2520 , 0 , 8339
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15 x 7 => 3360 , 0 , 5195
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15 x 8 => 4320 , 0 , 2061
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15 x 9 => 5400 , 0 , 364
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15 x 10 => 6600 , 0 , 0
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15 x 11 => 7920 , 0 , 0
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15 x 12 => 9360 , 0 , 0
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15 x 13 => 10920 , 0 , 0
-----------
15 x 14 => 12600 , 0 , 0
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15 x 15 => 14400 , 0 , 0
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15 x 16 => 16320 , 0 , 0
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15 x 17 => 18360 , 0 , 0
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15 x 18 => 20520 , 0 , 0
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15 x 19 => 22800 , 0 , 0
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15 x 20 => 25200 , 0 , 0
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16 x 1 => 136 , 325 , 13845
-----------
16 x 2 => 408 , 90 , 16605
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16 x 3 => 816 , 0 , 13374
-----------
16 x 4 => 1360 , 0 , 11460
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16 x 5 => 2040 , 0 , 9864
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16 x 6 => 2856 , 0 , 7653
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16 x 7 => 3808 , 0 , 4925
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16 x 8 => 4896 , 0 , 2058
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16 x 9 => 6120 , 0 , 297
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16 x 10 => 7480 , 0 , 0
-----------
16 x 11 => 8976 , 0 , 0
-----------
16 x 12 => 10608 , 0 , 0
-----------
16 x 13 => 12376 , 0 , 0
-----------
16 x 14 => 14280 , 0 , 0
-----------
16 x 15 => 16320 , 0 , 0
-----------
16 x 16 => 18496 , 0 , 0
-----------
16 x 17 => 20808 , 0 , 0
-----------
16 x 18 => 23256 , 0 , 0
-----------
16 x 19 => 25840 , 0 , 0
-----------
16 x 20 => 28560 , 0 , 0
-----------
17 x 1 => 153 , 348 , 14848
-----------
17 x 2 => 459 , 57 , 13107
-----------
17 x 3 => 918 , 0 , 12654
-----------
17 x 4 => 1530 , 0 , 10185
-----------
17 x 5 => 2295 , 0 , 8425
-----------
17 x 6 => 3213 , 0 , 7022
-----------
17 x 7 => 4284 , 0 , 3998
-----------
17 x 8 => 5508 , 0 , 1572
-----------
17 x 9 => 6885 , 0 , 224
-----------
17 x 10 => 8415 , 0 , 0
-----------
17 x 11 => 10098 , 0 , 0
-----------
17 x 12 => 11934 , 0 , 0
-----------
17 x 13 => 13923 , 0 , 0
-----------
17 x 14 => 16065 , 0 , 0
-----------
17 x 15 => 18360 , 0 , 0
-----------
17 x 16 => 20808 , 0 , 0
-----------
17 x 17 => 23409 , 0 , 0
-----------
17 x 18 => 26163 , 0 , 0
-----------
17 x 19 => 29070 , 0 , 0
-----------
17 x 20 => 32130 , 0 , 0
-----------
18 x 1 => 171 , 276 , 11796
-----------
18 x 2 => 513 , 36 , 11840
-----------
18 x 3 => 1026 , 0 , 11112
-----------
18 x 4 => 1710 , 0 , 9673
-----------