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%I #9 Jun 18 2022 23:37:36
%S 40,100,100,208,208,208,520,380,380,520,1120,844,632,844,1120,2800,
%T 1660,1280,1280,1660,2800,6208,3844,2344,2344,2344,3844,6208,15520,
%U 8012,5096,3952,3952,5096,8012,15520,35200,19060,10088,7936,6232,7936,10088,19060
%N T(n,k) is the number of (n+1) X (k+1) 0..4 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 40 100 208 520 1120 2800 6208 15520 35200 88000 203008
%C 100 208 380 844 1660 3844 8012 19060 41500 100468 225740
%C 208 380 632 1280 2344 5096 10088 23000 48328 113720 249512
%C 520 844 1280 2344 3952 7936 14672 31504 62800 141424 298640
%C 1120 1660 2344 3952 6232 11704 20440 41704 79480 172360 352024
%C 2800 3844 5096 7936 11704 20440 33464 64168 115480 238024 463736
%C 6208 8012 10088 14672 20440 33464 51800 93992 160888 317192 593048
%C 15520 19060 23000 31504 41704 64168 93992 160888 260680 487960 867560
%C 35200 41500 48328 62800 79480 115480 160888 260680 401560 716200 1215928
%C 88000 100468 113720 141424 172360 238024 317192 487960 716200 1215928 1966280
%C Empirical: T(n,k) is the number of (n+1) X (k+1) 0..3+i arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3+2*i, for i=1..3(..?).
%H R. H. Hardin, <a href="/A235280/b235280.txt">Table of n, a(n) for n = 1..420</a>
%F Empirical for column k (the k=2..9 recurrence also works for k=1; apparently all rows and columns satisfy the same order 9 recurrence):
%F diagonal: [linear recurrence of order 11, computed assuming that all rows and columns satisfy the same order 9 recurrence].
%F k=1: a(n) = 10*a(n-2) -24*a(n-4).
%F k=2..9: [same order 9 recurrence].
%e Some solutions for n=4, k=4:
%e 3 1 2 1 3 1 2 1 2 0 4 1 4 3 4 1 3 2 3 0
%e 1 4 0 4 1 4 0 4 0 3 0 2 0 4 0 3 0 4 0 2
%e 4 2 3 2 4 3 4 3 4 2 4 1 4 3 4 2 4 3 4 1
%e 1 4 0 4 1 4 0 4 0 3 0 2 0 4 0 3 0 4 0 2
%e 3 1 2 1 3 1 2 1 2 0 3 0 3 2 3 1 3 2 3 0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 05 2014