A234557 - OEIS

A234557

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 4 (constant-stress 1 X 1 tilings).

%I #11 Jun 20 2022 21:31:29

%S 70,220,618,1954,5506,17518,49506,158518,449170,1447510,4111458,

%T 13334374,37954546,123863638,353202306,1159606918,3311711890,

%U 10935135670,31268536098,103805608294,297121857586,991365572758,2839736979906

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

%H R. H. Hardin, <a href="/A234557/b234557.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 18*a(n-2) - 54*a(n-3) - 80*a(n-4) + 240*a(n-5).

%F Empirical g.f.: 2*x*(35 + 5*x - 651*x^2 - 40*x^3 + 3000*x^4) / ((1 - 3*x)*(1 - 8*x^2)*(1 - 10*x^2)). - _Colin Barker_, Oct 15 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 1 of A234564.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 28 2013