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 A234651 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 4 (constant-stress 1 X 1 tilings). 1

%I #11 Jun 20 2022 21:31:17

%S 160,728,3264,15008,67840,315008,1434624,6722048,30822400,145614848,

%T 671760384,3197247488,14829813760,71052197888,331140562944,

%U 1595912880128,7469054033920,36183831216128,169965785186304,827149902675968

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

%H R. H. Hardin, <a href="/A234651/b234651.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 44*a(n-2) - 176*a(n-3) - 480*a(n-4) + 1920*a(n-5).

%F Empirical g.f.: 8*x*(20 + 11*x - 836*x^2 - 240*x^3 + 8640*x^4) / ((1 - 4*x)*(1 - 20*x^2)*(1 - 24*x^2)). - _Colin Barker_, Oct 15 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 1 of A234658.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2013

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