A282785 - OEIS

%I #7 Feb 21 2019 06:40:04

%S 0,0,8,16,72,240,736,2352,7128,21424,63768,187424,547136,1586016,

%T 4570280,13105488,37414632,106404944,301580704,852159120,2401326712,

%U 6750087408,18931901880,52989773184,148039566336,412873929408,1149659579720

%N Number of n X 2 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

%H R. H. Hardin, <a href="/A282785/b282785.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 5*a(n-2)  +2*a(n-3) - 17*a(n-4) - 24*a(n-5) - 16*a(n-6).

%F Empirical g.f.: 8*x^3 / (1 - x - 3*x^2 - 4*x^3)^2. - _Colin Barker_, Feb 21 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A282791.

%K nonn

%O 1,3

%A _R. H. Hardin_, Feb 21 2017