A235274 - OEIS

A235274

Number of (n+1) X (4+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).

%I #10 Jun 18 2022 23:45:26

%S 520,844,1280,2344,3952,7936,14672,31504,62800,141424,298640,695344,

%T 1530832,3647536,8265872,20008624,46236880,113126704,264832400,

%U 652640944,1540956112,3815788336,9060105872,22507117744,53636823760,133528827184

%N Number of (n+1) X (4+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="/A235274/b235274.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*(130 + 81*x - 1841*x^2 - 949*x^3 + 9167*x^4 + 3486*x^5 - 19026*x^6 - 4032*x^7 + 13824*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 0 4 0 4 0 2 4 3 4 3 2 0 1 0 4 2 4 0 4 2

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

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

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

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

%Y Column 4 of A235280.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 05 2014