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%I #6 Jun 20 2022 21:01:17
%S 112,404,404,1264,1152,1264,4568,2924,2924,4568,14368,9108,6328,9108,
%T 14368,52016,25292,17312,17312,25292,52016,164416,82956,43240,41832,
%U 43240,82956,164416,596192,243164,129848,93680,93680,129848,243164
%N 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 5 (constant-stress 1 X 1 tilings).
%C Table starts
%C 112 404 1264 4568 14368 52016 164416 596192
%C 404 1152 2924 9108 25292 82956 243164 823836
%C 1264 2924 6328 17312 43240 129848 354856 1129256
%C 4568 9108 17312 41832 93680 254784 639440 1878960
%C 14368 25292 43240 93680 191128 476648 1109272 3039128
%C 52016 82956 129848 254784 476648 1092120 2354408 5995464
%C 164416 243164 354856 639440 1109272 2354408 4736536 11294552
%C 596192 823836 1129256 1878960 3039128 5995464 11294552 25287288
%C 1892992 2495084 3265864 5098448 7775608 14369096 25494136 53827832
%C 6874304 8636892 10806344 15829008 22805432 39500136 66161144 132005016
%H R. H. Hardin, <a href="/A234681/b234681.txt">Table of n, a(n) for n = 1..260</a>
%F Empirical for column k (the k=2..7 order 18 recurrence also works for k=1; apparently all rows and columns satisfy the same order 18 recurrence):
%F k=1: a(n) = 22*a(n-2) -120*a(n-4).
%F k=2..7: [same order 18 recurrence].
%e Some solutions for n=5, k=4:
%e 1 4 2 5 0 5 1 5 2 5 2 5 3 5 3 1 5 4 5 3
%e 2 0 3 1 1 1 2 1 3 1 2 0 3 0 3 1 0 4 0 3
%e 1 4 2 5 0 4 0 4 1 4 0 3 1 3 1 1 5 4 5 3
%e 4 2 5 3 3 2 3 2 4 2 2 0 3 0 3 1 0 4 0 3
%e 1 4 2 5 0 4 0 4 1 4 2 5 3 5 3 1 5 4 5 3
%e 2 0 3 1 1 0 1 0 2 0 3 1 4 1 4 2 1 5 1 4
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 29 2013