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A235087
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T(n,k) is the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
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9
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38, 90, 90, 202, 198, 202, 478, 418, 418, 478, 1078, 930, 830, 930, 1078, 2554, 2002, 1758, 1758, 2002, 2554, 5786, 4514, 3610, 3558, 3610, 4514, 5786, 13726, 9838, 7810, 7046, 7046, 7810, 9838, 13726, 31238, 22402, 16390, 14702, 13446, 14702, 16390
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OFFSET
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1,1
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COMMENTS
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Table starts
38 90 202 478 1078 2554 5786 13726 31238 74202
90 198 418 930 2002 4514 9838 22402 49294 113086
202 418 830 1758 3610 7810 16390 36014 76770 170682
478 930 1758 3558 7046 14702 29970 63862 132746 287122
1078 2002 3610 7046 13446 27218 53882 111782 226726 478402
2554 4514 7810 14702 27218 53590 103702 210318 418838 866298
5786 9838 16390 29970 53882 103702 196302 390578 764386 1553646
13726 22402 36014 63862 111782 210318 390578 763814 1474106 2953922
31238 49294 76770 132746 226726 418838 764386 1474106 2809478 5563846
74202 113086 170682 287122 478402 866298 1553646 2953922 5563846 10902494
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LINKS
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FORMULA
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Empirical for column k (k=4..7 recurrence works for k=1..3 also; apparently all rows and columns satisfy the same order 16 recurrence):
k=1: a(n) = 2*a(n-1) +6*a(n-2) -10*a(n-3) -5*a(n-4).
k=2: [order 10].
k=3: [order 15].
k=4..7: [same order 16 recurrence].
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EXAMPLE
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Some solutions for n=5, k=4:
0 2 1 2 0 2 4 2 4 1 1 4 2 3 0 1 3 0 3 0
3 1 4 1 3 4 2 4 2 3 3 2 4 1 2 2 0 1 0 1
2 4 3 4 2 1 3 1 3 0 1 4 2 3 0 1 3 0 3 0
3 1 4 1 3 2 0 2 0 1 3 2 4 1 2 4 2 3 2 3
1 3 2 3 1 1 3 1 3 0 1 4 2 3 0 1 3 0 3 0
3 1 4 1 3 3 1 3 1 2 3 2 4 1 2 2 0 1 0 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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