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 A235271 Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5 (constant-stress 1 X 1 tilings). 1

%I

%S 40,100,208,520,1120,2800,6208,15520,35200,88000,203008,507520,

%T 1185280,2963200,6980608,17451520,41359360,103398400,246059008,

%U 615147520,1467965440,3669913600,8774238208,21935595520,52511211520,131278028800

%N Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A235271/b235271.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-2) - 24*a(n-4).

%F Conjectures from _Colin Barker_, Oct 17 2018: (Start)

%F G.f.: 4*x*(2 + 5*x)*(5 - 24*x^2) / ((1 - 2*x)*(1 + 2*x)*(1 - 6*x^2)).

%F a(n) = (-2)^n + 9*2^n + 6^((1/2)*(-1+n))*(12-12*(-1)^n + 5*sqrt(6) + 5*(-1)^n*sqrt(6)).

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A235280.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 05 2014

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Last modified November 27 01:14 EST 2022. Contains 358362 sequences. (Running on oeis4.)