A258918 - OEIS

A258918

Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum equal to the antidiagonal sum or central row sum equal to the central column sum.

%I #9 Dec 23 2018 08:14:42

%S 200,576,1680,5184,15840,46656,138240,419904,1270080,3779136,11275200,

%T 34012224,102409920,306110016,916090560,2754990144,8278407360,

%U 24794911296,74304112320,223154201664,669946334400,2008387814976

%N Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum equal to the antidiagonal sum or central row sum equal to the central column sum.

%H R. H. Hardin, <a href="/A258918/b258918.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 6*a(n-2) + 18*a(n-3).

%F Empirical g.f.: 8*x*(25 - 3*x + 144*x^2) / ((1 - 3*x)*(1 + 6*x^2)). - _Colin Barker_, Dec 23 2018

%e Some solutions for n=4:

%e ..0..1..1....1..1..0....1..0..0....1..0..0....1..0..1....1..0..0....0..0..1

%e ..1..0..0....0..1..1....0..1..1....1..0..1....1..1..1....1..1..0....0..1..0

%e ..1..1..1....1..1..1....1..0..1....0..0..0....1..0..0....0..0..0....1..1..0

%e ..0..0..0....1..0..0....0..0..0....1..1..0....0..1..1....0..0..0....0..1..1

%e ..1..1..0....0..1..1....1..1..0....1..0..0....0..0..1....1..1..0....0..1..0

%e ..0..0..1....0..0..0....1..0..0....0..1..1....1..1..0....1..0..0....1..0..0

%Y Column 1 of A258921.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 14 2015