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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 5 (constant-stress 1 X 1 tilings).
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%I #6 Jun 20 2022 20:54:11

%S 232,1148,1148,5472,4416,5472,27344,16580,16580,27344,131200,69336,

%T 49480,69336,131200,661952,281612,174320,174320,281612,661952,3196416,

%U 1253088,603480,531984,603480,1253088,3196416,16276736,5385236,2377712,1602224

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

%C Table starts

%C 232 1148 5472 27344 131200 661952 3196416

%C 1148 4416 16580 69336 281612 1253088 5385236

%C 5472 16580 49480 174320 603480 2377712 9134920

%C 27344 69336 174320 531984 1602224 5614248 19258400

%C 131200 281612 603480 1602224 4224328 13220576 40731576

%C 661952 1253088 2377712 5614248 13220576 37361280 104366624

%C 3196416 5385236 9134920 19258400 40731576 104366624 265716040

%C 16276736 25119456 39076784 74809368 144171008 337733136 789826592

%C 79071232 112545548 161746392 282312464 498365320 1071197312 2311358136

%C 406166528 544181136 735721040 1187833176 1942449632 3852945648 7703580416

%H R. H. Hardin, <a href="/A234690/b234690.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k (column 3..5 order 29 recurrence also works for k=1..2; apparently all rows and columns satisfy the same order 29 recurrence):

%F k=1: a(n) = 72*a(n-2) -1712*a(n-4) +13440*a(n-6).

%F k=2: [order 24].

%F k=3..5: [same order 29].

%e Some solutions for n=3, k=4:

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 29 2013