A234667 - OEIS

A234667

Number of (n+1) X (1+1) 0..7 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 19 2022 01:04:30

%S 492,3816,29568,229272,1778412,13801056,107144508,832197192,

%T 6466444032,50269824456,390963554148,3042084148512,23680823914452,

%U 184429911964056,1437009243823488,11202089753841432,87364420495436172,681684020356757856

%N Number of (n+1) X (1+1) 0..7 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="/A234667/b234667.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) + 25*a(n-2) - 950*a(n-3) + 2091*a(n-4) + 7326*a(n-5) - 3780*a(n-6) - 10080*a(n-7).

%F Empirical g.f.: 12*x*(41 - 256*x - 3013*x^2 + 15610*x^3 + 35486*x^4 - 26880*x^5 - 53760*x^6) / ((1 - 8*x)*(1 - 6*x - 12*x^2)*(1 - 61*x^2 + 105*x^4)). - _Colin Barker_, Oct 16 2018

%e Some solutions for n=3:

%e 5 1 7 7 0 2 1 3 4 6 4 5 2 4 3 2 5 5 7 1

%e 1 1 0 4 0 6 4 2 0 6 4 1 4 2 2 5 3 7 7 5

%e 6 2 5 5 5 7 4 6 2 4 1 2 4 6 4 3 0 0 4 6

%e 5 5 2 6 2 0 6 4 7 5 0 5 6 4 7 2 3 7 0 6

%Y Column 1 of A234672.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2013