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%I #6 Jun 20 2022 20:38:14
%S 80,256,256,808,656,808,2580,1728,1728,2580,8184,4820,3832,4820,8184,
%T 26164,13624,9460,9460,13624,26164,83224,39884,23792,21264,23792,
%U 39884,83224,266572,117488,63884,48844,48844,63884,117488,266572,849688,354588
%N T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
%C Table starts
%C 80 256 808 2580 8184 26164 83224 266572 849688
%C 256 656 1728 4820 13624 39884 117488 354588 1072888
%C 808 1728 3832 9460 23792 63884 173440 491596 1403944
%C 2580 4820 9460 21264 48844 121768 306532 813576 2175660
%C 8184 13624 23792 48844 102336 238060 556560 1391140 3490704
%C 26164 39884 63884 121768 238060 524728 1160340 2765568 6585764
%C 83224 117488 173440 306532 556560 1160340 2420288 5516124 12489280
%C 266572 354588 491596 813576 1391140 2765568 5516124 12147808 26512228
%C 849688 1072888 1403944 2175660 3490704 6585764 12489280 26512228 55604120
%C 2726852 3306172 4134548 6047320 9185772 16502816 29986228 61672784 125443708
%H R. H. Hardin, <a href="/A235098/b235098.txt">Table of n, a(n) for n = 1..285</a>
%F Empirical for column k (the k=4..7 recurrence works also for k=1..3; apparently every row and column satisfies the same order 23 recurrence):
%F k=1: a(n) = 3*a(n-1) +13*a(n-2) -39*a(n-3) -26*a(n-4) +78*a(n-5).
%F k=2: [order 16].
%F k=3: [order 22].
%F k=4..7: [same order 23].
%e Some solutions for n=4, k=4:
%e 0 3 2 0 1 3 0 3 1 3 2 3 0 3 1 1 2 1 4 2
%e 1 0 3 5 2 1 2 1 3 1 4 1 2 1 3 4 1 4 3 5
%e 0 3 2 0 1 4 1 4 2 4 3 4 1 4 2 2 3 2 5 3
%e 1 0 3 5 2 1 2 1 3 1 4 1 2 1 3 4 1 4 3 5
%e 2 5 4 2 3 4 1 4 2 4 3 4 1 4 2 2 3 2 5 3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 03 2014
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