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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 2 (constant-stress 1 X 1 tilings).
7

%I #6 Jun 20 2022 20:48:47

%S 250,1834,1834,13464,17022,13464,99142,158288,158288,99142,728536,

%T 1483566,1856768,1483566,728536,5368636,13868952,22124316,22124316,

%U 13868952,5368636,39476802,130537496,260915944,337787398,260915944

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

%C Table starts

%C 250 1834 13464 99142 728536

%C 1834 17022 158288 1483566 13868952

%C 13464 158288 1856768 22124316 260915944

%C 99142 1483566 22124316 337787398 5086391644

%C 728536 13868952 260915944 5086391644 96676755176

%C 5368636 130537496 3122368992 78343976876 1903351845712

%C 39476802 1224977498 36940569778 1187892774098 36413811919636

%C 291119578 11577801970 443886085700 18458711626338 723978446690964

%C 2142048610 109063132114 5267872223782 281836734313650

%C 15807820384 1035175545192 63565110955752

%H R. H. Hardin, <a href="/A234497/b234497.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

%F k=1: a(n) = 5*a(n-1) +74*a(n-2) -295*a(n-3) -1008*a(n-4) +840*a(n-5).

%F k=2: [order 23].

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 26 2013