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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 4 (constant-stress 1 X 1 tilings).
6

%I #6 Jun 20 2022 20:32:22

%S 492,3816,3816,29568,28860,29568,229272,217968,217968,229272,1778412,

%T 1648188,1604020,1648188,1778412,13801056,12470688,11826092,11826092,

%U 12470688,13801056,107144508,94430072,87273500,85076140,87273500

%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 4 (constant-stress 1 X 1 tilings).

%C Table starts

%C 492 3816 29568 229272 1778412 13801056

%C 3816 28860 217968 1648188 12470688 94430072

%C 29568 217968 1604020 11826092 87273500 644848264

%C 229272 1648188 11826092 85076140 612823800 4421960468

%C 1778412 12470688 87273500 612823800 4310166424 30383174872

%C 13801056 94430072 644848264 4421960468 30383174872

%C 107144508 715532392 4769561472 31951474920

%C 832197192 5425977036 35319420856

%C 6466444032 41174389648

%C 50269824456

%H R. H. Hardin, <a href="/A234672/b234672.txt">Table of n, a(n) for n = 1..60</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 7].

%F k=2: [order 31].

%e Some solutions for n=2, k=4:

%e 6 0 5 3 4 2 0 6 0 3 4 2 0 0 6 0 2 4 6 3

%e 4 2 3 5 2 2 4 6 4 3 2 4 6 2 4 0 6 4 2 3

%e 0 2 7 5 6 4 2 0 2 5 4 2 0 0 6 4 6 0 2 7

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 29 2013