A204566 - OEIS

A204566

Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order.

%I #9 Jun 07 2018 11:59:41

%S 42,482,6112,80518,1075080,14421190,193752824,2604524150,35017728648,

%T 470841185510,6330966828952,85127273980246,1144638803080104,

%U 15391060969557190,206951592970169528,2782716926395505462

%N Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order.

%C Column 2 of A204572.

%H R. H. Hardin, <a href="/A204566/b204566.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 19*a(n-1) - 79*a(n-2) + 57*a(n-3) + 16*a(n-4) - 12*a(n-5).

%F Empirical g.f.: 2*x*(21 - 158*x + 136*x^2 + 37*x^3 - 30*x^4) / ((1 - x)*(1 - 5*x + 2*x^2)*(1 - 13*x - 6*x^2)). - _Colin Barker_, Jun 07 2018

%e Some solutions for n=4:

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

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

%e ..1..0..1....2..0..0....1..1..0....0..2..0....3..2..0....1..0..0....3..2..0

%e ..0..1..0....3..2..0....0..1..1....1..0..1....2..0..0....0..0..2....0..3..2

%e ..1..0..0....1..3..2....1..0..1....3..1..0....1..2..0....0..0..0....1..0..3

%Y Cf. A204572.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 16 2012