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A235301
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T(n,k) is the number of (n+1) X (k+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3 (constant-stress 1 X 1 tilings).
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12
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40, 108, 108, 272, 232, 272, 744, 476, 476, 744, 1888, 1132, 832, 1132, 1888, 5232, 2556, 1736, 1736, 2556, 5232, 13376, 6532, 3536, 3184, 3536, 6532, 13376, 37536, 15692, 8336, 5784, 5784, 8336, 15692, 37536, 96640, 42100, 18832, 12328, 9568
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OFFSET
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1,1
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COMMENTS
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Table starts
40 108 272 744 1888 5232 13376 37536 96640 274368
108 232 476 1132 2556 6532 15692 42100 104988 290932
272 476 832 1736 3536 8336 18832 48128 115952 312416
744 1132 1736 3184 5784 12328 25592 60856 138744 356632
1888 2556 3536 5784 9568 18624 35936 79728 172288 420816
5232 6532 8336 12328 18624 32992 58688 120112 242592 553552
13376 15692 18832 25592 35936 58688 97888 187184 358016 768272
37536 42100 48128 60856 79728 120112 187184 333952 603216 1215520
96640 104988 115952 138744 172288 242592 358016 603216 1044640 2006448
274368 290932 312416 356632 420816 553552 768272 1215520 2006448 3677632
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LINKS
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FORMULA
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Empirical for column k (the k=2..10 recurrence works for k=1; apparently all rows and columns satisfy the same order 10 recurrence):
diagonal: [linear recurrence of order 11, computed assuming all rows and columns satisfy the same order 10 recurrence]
k=1: a(n) = 14*a(n-2) -48*a(n-4).
k=2..10: [same order 10 recurrence]
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EXAMPLE
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Some solutions for n=5, k=4:
1 3 0 3 0 1 3 0 2 2 0 2 0 2 1 2 3 1 3 3
1 0 0 0 0 2 1 1 0 3 2 1 2 1 3 2 0 1 0 3
1 3 0 3 0 1 3 0 2 2 0 2 0 2 1 2 3 1 3 3
3 2 2 2 2 2 1 1 0 3 2 1 2 1 3 2 0 1 0 3
1 3 0 3 0 1 3 0 2 2 1 3 1 3 2 1 2 0 2 2
3 2 2 2 2 2 1 1 0 3 1 0 1 0 2 2 0 1 0 3
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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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