A235081 - OEIS

A235081

Number of (n+1) X (2+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%I #9 Jun 19 2022 01:31:36

%S 90,198,418,930,2002,4514,9838,22402,49294,113086,250886,579046,

%T 1294282,3002798,6759506,15755762,35708898,83589666,190685374,

%U 448116834,1028599870,2425881086,5600857366,13251905638,30761769178,72994149742

%N Number of (n+1) X (2+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%H R. H. Hardin, <a href="/A235081/b235081.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 10*a(n-2) - 33*a(n-3) - 28*a(n-4) + 111*a(n-5) + 20*a(n-6) - 111*a(n-7) - 27*a(n-8) + 30*a(n-9) + 10*a(n-10).

%F Empirical g.f.: 2*x*(45 - 36*x - 538*x^2 + 333*x^3 + 2043*x^4 - 722*x^5 - 2554*x^6 - 257*x^7 + 772*x^8 + 226*x^9) / ((1 - x - x^2)*(1 - 2*x - x^2)*(1 - 5*x^2)*(1 - 5*x^2 + 2*x^4)). - _Colin Barker_, Oct 17 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 2 of A235087.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 03 2014