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T(n,k) is the number of (n+1) X (k+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
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%I #7 Jun 19 2022 00:00:47

%S 120,420,420,1328,1288,1328,4652,3688,3688,4652,14944,11728,9656,

%T 11728,14944,52468,34916,28400,28400,34916,52468,170864,113940,78824,

%U 77368,78824,113940,170864,601100,348876,241456,201676,201676,241456,348876

%N T(n,k) is the number of (n+1) X (k+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%C Table starts

%C 120 420 1328 4652 14944 52468 170864 601100

%C 420 1288 3688 11728 34916 113940 348876 1158552

%C 1328 3688 9656 28400 78824 241456 698304 2200992

%C 4652 11728 28400 77368 201676 580668 1593940 4773744

%C 14944 34916 78824 201676 496520 1355796 3548456 10155532

%C 52468 113940 241456 580668 1355796 3512000 8787924 24042932

%C 170864 348876 698304 1593940 3548456 8787924 21123784 55565636

%C 601100 1158552 2200992 4773744 10155532 24042932 55565636 140450408

%C 1980544 3626376 6566416 13619216 27803624 63316120 141304528 345065744

%C 6979348 12193672 21133848 41986384 82397748 180522036 389137436 917415816

%H R. H. Hardin, <a href="/A235239/b235239.txt">Table of n, a(n) for n = 1..198</a>

%F Empirical for column k (the k=4..6 recurrence works also for k=1..3; apparently all rows and columns satisfy the same order 41 recurrence):

%F k=1: [linear recurrence of order 8].

%F k=2: [order 28].

%F k=3: [order 40].

%F k=4..6: [same order 41 recurrence].

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

%e 1 0 1 0 2 2 0 3 0 5 1 3 0 4 2 6 1 3 2 6

%e 0 5 0 5 1 1 5 2 5 4 5 1 4 2 6 3 4 0 5 3

%e 5 4 5 4 6 3 1 4 1 6 2 4 1 5 3 6 1 3 2 6

%e 1 6 1 6 2 1 5 2 5 4 5 1 4 2 6 3 4 0 5 3

%e 5 4 5 4 6 3 1 4 1 6 3 5 2 6 4 6 1 3 2 6

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 05 2014