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%I #6 Jun 20 2022 20:52:38
%S 20,46,46,104,88,104,244,170,170,244,560,358,292,358,560,1336,754,560,
%T 560,754,1336,3104,1690,1100,988,1100,1690,3104,7504,3746,2324,1816,
%U 1816,2324,3746,7504,17600,8722,4924,3616,3188,3616,4924,8722,17600,42976
%N 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).
%C Table starts
%C 20 46 104 244 560 1336 3104 7504 17600 42976 101504
%C 46 88 170 358 754 1690 3746 8722 19906 47458 110210
%C 104 170 292 560 1100 2324 4924 10988 24284 56060 127132
%C 244 358 560 988 1816 3616 7304 15544 33064 73288 161000
%C 560 754 1100 1816 3188 6076 11876 24340 50180 107044 227780
%C 1336 1690 2324 3616 6076 11140 21164 42076 84556 174700 361484
%C 3104 3746 4924 7304 11876 21164 39508 77060 152564 308756 627124
%C 7504 8722 10988 15544 24340 42076 77060 147892 289444 577732 1159268
%C 17600 19906 24284 33064 50180 84556 152564 289444 562580 1114036 2220884
%C 42976 47458 56060 73288 107044 174700 308756 577732 1114036 2191828 4349300
%C 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.
%H R. H. Hardin, <a href="/A234266/b234266.txt">Table of n, a(n) for n = 1..541</a>
%F Empirical for column k (k=2 recurrence also works for k=1; apparently all rows and columns have the same order 6 recurrence):
%F k=1: a(n) = 2*a(n-1) +6*a(n-2) -12*a(n-3).
%F 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).
%e Some solutions for n=5, k=4:
%e 0 2 0 2 0 0 2 2 2 0 2 2 1 2 1 0 2 0 2 0
%e 2 2 2 2 2 0 0 2 0 0 2 0 1 0 1 2 2 2 2 2
%e 2 0 2 0 2 0 2 2 2 0 1 1 0 1 0 2 0 2 0 2
%e 2 2 2 2 2 0 0 2 0 0 2 0 1 0 1 0 0 0 0 0
%e 0 2 0 2 0 2 0 0 0 2 1 1 0 1 0 0 2 0 2 0
%e 1 1 1 1 1 0 0 2 0 0 2 0 1 0 1 1 1 1 1 1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 22 2013