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%I #6 Jun 20 2022 20:44:54
%S 40,120,120,376,360,376,1200,1128,1128,1200,3848,3912,3684,3912,3848,
%T 12360,13368,13336,13336,13368,12360,39720,47980,49056,55492,49056,
%U 47980,39720,127664,169128,186500,221272,221272,186500,169128,127664,410344
%N T(n,k) is the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
%C Table starts
%C 40 120 376 1200 3848 12360 39720
%C 120 360 1128 3912 13368 47980 169128
%C 376 1128 3684 13336 49056 186500 710304
%C 1200 3912 13336 55492 221272 990956 4151672
%C 3848 13368 49056 221272 991144 4834440 22970144
%C 12360 47980 186500 990956 4834440 28854040 150606424
%C 39720 169128 710304 4151672 22970144 150606424 911837036
%C 127664 615344 2755840 19178920 115287720 948274980 6251426440
%C 410344 2208840 10693364 82629808 562322520 5093099972 39266933948
%C 1318968 8101636 42087616 389619632 2874164624 33282246680 276635826688
%H R. H. Hardin, <a href="/A234921/b234921.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -2*a(n-2) -2*a(n-3) +a(n-4).
%F k=2: [order 13].
%F k=3: [order 19].
%F k=4: [order 54].
%e Some solutions for n=4, k=4:
%e 3 2 1 2 1 2 3 0 3 0 4 3 1 3 4 3 0 1 2 3
%e 2 3 0 3 0 1 4 3 4 3 3 4 0 4 3 4 3 2 1 0
%e 3 2 1 2 1 2 3 4 3 4 4 3 1 3 0 3 4 1 2 3
%e 0 1 2 1 2 1 0 3 4 3 3 4 0 4 3 2 1 0 3 2
%e 1 0 3 0 3 4 1 2 1 2 0 3 1 3 4 3 0 1 2 3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 01 2014
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