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A234266
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T(n,k) is the number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2 (constant-stress 1 X 1 tilings).
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9
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20, 46, 46, 104, 88, 104, 244, 170, 170, 244, 560, 358, 292, 358, 560, 1336, 754, 560, 560, 754, 1336, 3104, 1690, 1100, 988, 1100, 1690, 3104, 7504, 3746, 2324, 1816, 1816, 2324, 3746, 7504, 17600, 8722, 4924, 3616, 3188, 3616, 4924, 8722, 17600, 42976
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OFFSET
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1,1
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COMMENTS
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Table starts
20 46 104 244 560 1336 3104 7504 17600 42976 101504
46 88 170 358 754 1690 3746 8722 19906 47458 110210
104 170 292 560 1100 2324 4924 10988 24284 56060 127132
244 358 560 988 1816 3616 7304 15544 33064 73288 161000
560 754 1100 1816 3188 6076 11876 24340 50180 107044 227780
1336 1690 2324 3616 6076 11140 21164 42076 84556 174700 361484
3104 3746 4924 7304 11876 21164 39508 77060 152564 308756 627124
7504 8722 10988 15544 24340 42076 77060 147892 289444 577732 1159268
17600 19906 24284 33064 50180 84556 152564 289444 562580 1114036 2220884
42976 47458 56060 73288 107044 174700 308756 577732 1114036 2191828 4349300
Empirical: also number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 6.
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LINKS
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FORMULA
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Empirical for column k (k=2 recurrence also works for k=1; apparently all rows and columns have the same order 6 recurrence):
k=1: a(n) = 2*a(n-1) +6*a(n-2) -12*a(n-3).
k=2..7: a(n) = 3*a(n-1) +6*a(n-2) -24*a(n-3) +4*a(n-4) +36*a(n-5) -24*a(n-6).
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EXAMPLE
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Some solutions for n=5, k=4:
0 2 0 2 0 0 2 2 2 0 2 2 1 2 1 0 2 0 2 0
2 2 2 2 2 0 0 2 0 0 2 0 1 0 1 2 2 2 2 2
2 0 2 0 2 0 2 2 2 0 1 1 0 1 0 2 0 2 0 2
2 2 2 2 2 0 0 2 0 0 2 0 1 0 1 0 0 0 0 0
0 2 0 2 0 2 0 0 0 2 1 1 0 1 0 0 2 0 2 0
1 1 1 1 1 0 0 2 0 0 2 0 1 0 1 1 1 1 1 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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