A205356 - OEIS

A205356

Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having the same number of equal diagonal or antidiagonal elements, and new values 0..2 introduced in row major order.

%I #9 Jun 11 2018 14:49:47

%S 194,1562,12866,107330,904514,7690946,65916482,568956866,4941735746,

%T 43157726402,378706958402,3336772020674,29503215149378,

%U 261638552102594,2326066810503746,20723166492924866,184949755175942978

%N Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having the same number of equal diagonal or antidiagonal elements, and new values 0..2 introduced in row major order.

%C Column 3 of A205361.

%H R. H. Hardin, <a href="/A205356/b205356.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 23*a(n-1) - 187*a(n-2) + 645*a(n-3) - 912*a(n-4) + 432*a(n-5).

%F Empirical g.f.: 2*x*(97 - 1450*x + 6609*x^2 - 10812*x^3 + 5652*x^4) / ((1 - x)*(1 - 4*x)*(1 - 9*x)*(1 - 9*x + 12*x^2)). - _Colin Barker_, Jun 11 2018

%e Some solutions for n=4:

%e ..0..1..1..2....0..0..0..0....0..0..0..0....0..1..0..2....0..0..1..0

%e ..0..2..0..2....0..0..0..0....0..1..0..1....1..2..1..0....0..2..0..2

%e ..1..1..1..1....0..0..0..0....1..2..1..2....1..1..1..1....2..1..2..1

%e ..2..2..0..0....0..0..0..0....1..1..0..1....0..1..2..1....2..2..2..2

%e ..0..1..1..1....0..0..0..0....1..2..1..1....0..0..1..0....2..1..2..0

%Y Cf. A205361.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 26 2012