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%I #6 Jun 20 2022 20:33:36
%S 62,242,242,944,926,944,3686,3540,3540,3686,14402,13554,13260,13554,
%T 14402,56312,51950,49784,49784,51950,56312,220334,199340,187196,
%U 183422,187196,199340,220334,862706,765738,705072,677138,677138,705072,765738
%N 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 2 (constant-stress 1 X 1 tilings).
%C Table starts
%C 62 242 944 3686 14402 56312 220334
%C 242 926 3540 13554 51950 199340 765738
%C 944 3540 13260 49784 187196 705072 2659824
%C 3686 13554 49784 183422 677138 2505400 9288710
%C 14402 51950 187196 677138 2455350 8928348 32545706
%C 56312 199340 705072 2505400 8928348 31925284 114484712
%C 220334 765738 2659824 9288710 32545706 114484712 404043442
%C 862706 2944686 10049936 34509914 118945534 411823840 1431125914
%C 3380192 11336132 38030588 128461544 435728940 1485448976 5084793448
%C 13252982 43687010 144134184 479146446 1600124066 5373690488 18127421166
%H R. H. Hardin, <a href="/A234490/b234490.txt">Table of n, a(n) for n = 1..179</a>
%F Empirical for column k:
%F k=1: a(n) = 7*a(n-1) -9*a(n-2) -12*a(n-3).
%F k=2: a(n) = 10*a(n-1) -28*a(n-2) +a(n-3) +54*a(n-4) +24*a(n-5).
%F k=3: [order 11].
%F k=4: [order 18].
%F k=5: [order 31].
%e Some solutions for n=4, k=4:
%e 2 2 0 2 1 0 3 0 1 2 0 0 2 3 2 0 1 2 2 2
%e 3 1 1 1 2 2 3 2 1 0 1 3 3 2 3 3 2 1 3 1
%e 1 1 3 1 0 1 0 1 2 3 1 1 3 0 3 1 2 3 3 3
%e 0 2 2 2 3 0 1 0 3 2 0 2 2 1 2 0 3 2 0 2
%e 3 3 1 3 2 0 3 0 1 2 0 0 2 3 2 2 3 0 0 0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 26 2013
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