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A235310
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T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6 (constant-stress 1 X 1 tilings).
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9
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70, 210, 210, 518, 518, 518, 1554, 1106, 1106, 1554, 4006, 2918, 2118, 2918, 4006, 12018, 6786, 5042, 5042, 6786, 12018, 32006, 18662, 10790, 10790, 10790, 18662, 32006, 96018, 46226, 27602, 21090, 21090, 27602, 46226, 96018, 261670, 130598
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OFFSET
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1,1
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COMMENTS
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Table starts
70 210 518 1554 4006 12018 32006 96018 261670
210 518 1106 2918 6786 18662 46226 130598 338370
518 1106 2118 5042 10790 27602 64326 172658 428198
1554 2918 5042 10790 21090 49574 107186 269222 629154
4006 6786 10790 21090 38182 83394 168998 400674 889126
12018 18662 27602 49574 83394 168998 319826 711206 1486338
32006 46226 64326 107186 168998 319826 568902 1192946 2360486
96018 130598 172658 269222 400674 711206 1192946 2360486 4418658
261670 338370 428198 629154 889126 1486338 2360486 4418658 7845670
785010 973478 1187666 1656998 2238786 3544742 5359826 9528998 16106370
Empirical: T(n,k) is the number of (n+1) X (k+1) 0..4+i arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4+2*i (constant-stress 1 X 1 tilings), for i=1..3(..?).
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LINKS
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FORMULA
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Empirical for column k (the k=2..7 recurrence also works for k=1; apparently all rows and columns satisfy the same order 14 recurrence):
k=1: a(n) = 3*a(n-1) +13*a(n-2) -39*a(n-3) -40*a(n-4) +120*a(n-5)
k=2..7: [same order 14 recurrence]
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EXAMPLE
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Some solutions for n=5, k=4:
0 3 0 4 0 5 2 5 2 5 3 5 0 5 3 5 1 5 2 5
5 2 5 3 5 2 5 2 5 2 4 0 1 0 4 0 2 0 3 0
1 4 1 5 1 3 0 3 0 3 3 5 0 5 3 4 0 4 1 4
3 0 3 1 3 1 4 1 4 1 4 0 1 0 4 0 2 0 3 0
0 3 0 4 0 3 0 3 0 3 3 5 0 5 3 4 0 4 1 4
4 1 4 2 4 1 4 1 4 1 5 1 2 1 5 1 3 1 4 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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