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A234883 Number of (n+1) X (1+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings). 1

%I #11 Jun 19 2022 01:18:50

%S 80,272,856,2896,9192,31064,98696,333456,1059616,3579832,11375904,

%T 38432120,122129480,412598472,1311156208,4429566640,14076290136,

%U 47554864016,151120001288,510538698456,1622391563368,5481032709232

%N Number of (n+1) X (1+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234883/b234883.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-2) - 37*a(n-4) + 21*a(n-6).

%F Empirical g.f.: 8*x*(10 + 34*x - 33*x^2 - 114*x^3 + 21*x^4 + 73*x^5) / (1 - 14*x^2 + 37*x^4 - 21*x^6). - _Colin Barker_, Oct 16 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A234890.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2014

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