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Number of (n+1) X (5+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 #10 Jun 18 2022 23:45:21

%S 1120,1660,2344,3952,6232,11704,20440,41704,79480,172360,352024,

%T 797512,1714552,4006024,8930200,21319624,48718840,118055560,274305304,

%U 671516872,1577623672,3888983944,9203383960,22793395144,54200318200,134655258760

%N Number of (n+1) X (5+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="/A235275/b235275.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 15*a(n-2) - 15*a(n-3) - 80*a(n-4) + 80*a(n-5) + 180*a(n-6) - 180*a(n-7) - 144*a(n-8) + 144*a(n-9).

%F Empirical g.f.: 4*x*(280 + 135*x - 4029*x^2 - 1623*x^3 + 20405*x^4 + 6138*x^5 - 43086*x^6 - 7344*x^7 + 31824*x^8) / ((1 - x)*(1 - 2*x)*(1 + 2*x)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - 6*x^2)). - _Colin Barker_, Oct 18 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 5 of A235280.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 05 2014