A208376 - OEIS

%I #9 Jul 02 2018 05:46:01

%S 16,256,704,1344,2176,3200,4416,5824,7424,9216,11200,13376,15744,

%T 18304,21056,24000,27136,30464,33984,37696,41600,45696,49984,54464,

%U 59136,64000,69056,74304,79744,85376,91200,97216,103424,109824,116416,123200,130176

%N Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%C Column 5 of A208379.

%H R. H. Hardin, <a href="/A208376/b208376.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 96*n^2 - 32*n - 64 for n>1.

%F Conjectures from _Colin Barker_, Jul 02 2018: (Start)

%F G.f.: 16*x*(1 + 13*x - x^2 - x^3) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208379.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2012