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%I #7 Jun 20 2022 20:26:02
%S 168,672,672,2184,2184,2184,8736,6048,6048,8736,29976,21048,14760,
%T 21048,29976,119904,64320,45792,45792,64320,119904,426120,233016,
%U 127032,127032,127032,233016,426120,1704480,760608,423072,319488,319488,423072,760608
%N T(n,k) is the number of (n+1) X (k+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 8 (constant-stress 1 X 1 tilings).
%C Table starts
%C 168 672 2184 8736 29976 119904 426120 1704480
%C 672 2184 6048 21048 64320 233016 760608 2827992
%C 2184 6048 14760 45792 127032 423072 1283880 4481376
%C 8736 21048 45792 127032 319488 972888 2723040 8836536
%C 29976 64320 127032 319488 737160 2072256 5395128 16400256
%C 119904 233016 423072 972888 2072256 5395128 13083552 37239960
%C 426120 760608 1283880 2723040 5395128 13083552 29705640 79520352
%C 1704480 2827992 4481376 8836536 16400256 37239960 79520352 200901240
%C 6197208 9650112 14469624 26699136 46685256 99668544 200901240 480387840
%C 24788832 36532344 52195488 90688728 150256320 302942136 578901408 1314864792
%H R. H. Hardin, <a href="/A234738/b234738.txt">Table of n, a(n) for n = 1..196</a>
%F Empirical for column k (the k=2 recurrence also works for column 1; apparently every row and column satisfies the same order 23 recurrence):
%F k=1: a(n) = 4*a(n-1) +34*a(n-2) -136*a(n-3) -369*a(n-4) +1476*a(n-5) +1260*a(n-6) -5040*a(n-7).
%F k=2..6: [same order 23 recurrence].
%e Some solutions for n=4, k=4:
%e 5 2 4 2 5 4 2 5 0 5 7 4 6 3 6 7 1 6 2 7
%e 2 7 1 7 2 1 7 2 5 2 2 7 1 6 1 1 3 0 4 1
%e 3 0 2 0 3 4 2 5 0 5 5 2 4 1 4 6 0 5 1 6
%e 1 6 0 6 1 1 7 2 5 2 1 6 0 5 0 1 3 0 4 1
%e 4 1 3 1 4 4 2 5 0 5 7 4 6 3 6 7 1 6 2 7
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 30 2013
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