A297079 - OEIS

%I #8 Feb 26 2019 08:20:44

%S 4,12,30,96,286,848,2620,7964,24332,74740,228968,702656,2157520,

%T 6622672,20336808,62452688,191784960,588994592,1808876976,5555328528,

%U 17061469024,52399035584,160927919584,494243002176,1517923151392,4661861611200

%N Number of n X 2 0..1 arrays with no 1 adjacent to 2 king-move neighboring 1s.

%H R. H. Hardin, <a href="/A297079/b297079.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 4*a(n-3) - 14*a(n-4) - 14*a(n-5) - 4*a(n-6).

%F Empirical g.f.: 2*x*(2 + 2*x - 5*x^2 - 14*x^3 - 9*x^4 - 2*x^5) / (1 - 2*x - 4*x^2 - 4*x^3 + 14*x^4 + 14*x^5 + 4*x^6). - _Colin Barker_, Feb 26 2019

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 2 of A297085.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 25 2017