A235312 - OEIS

A235312

Number of (n+1) X (1+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7 (constant-stress 1 X 1 tilings).

%I #10 Jun 18 2022 23:07:47

%S 112,392,1120,3920,11776,41216,128128,448448,1426432,4992512,16130560,

%T 56456960,184446976,645564416,2126645248,7443258368,24679432192,

%U 86378012672,287911321600,1007689625600,3373484670976,11807196348416

%N Number of (n+1) X (1+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A235312/b235312.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 28*a(n-2) -252*a(n-4) +720*a(n-6).

%F Empirical g.f.: 8*x*(2 + 7*x)*(7 - 126*x^2 + 540*x^4) / ((1 - 6*x^2)*(1 - 10*x^2)*(1 - 12*x^2)). - _Colin Barker_, Oct 18 2018

%e Some solutions for n=4:

%e 4 2 6 2 3 2 2 3 1 2 4 0 5 0 5 0 3 5 3 0

%e 0 5 0 3 0 6 6 0 6 0 1 4 0 2 2 4 6 1 1 5

%e 3 1 5 1 6 5 5 6 4 5 5 1 5 0 6 1 3 5 6 3

%e 1 6 0 3 0 6 6 0 6 0 0 3 3 5 3 5 6 1 2 6

%e 4 2 4 0 2 1 5 6 5 6 5 1 5 0 5 0 2 4 3 0

%Y Column 1 of A235319.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 05 2014