A280227 - OEIS

%I #8 Feb 13 2019 08:05:14

%S 0,4,6,8,14,24,42,72,124,212,362,616,1046,1772,2996,5056,8518,14328,

%T 24066,40368,67628,113164,189154,315848,526894,878164,1462372,2433272,

%U 4045694,6721752,11160282,18517656,30706396,50888132,84287066,139531816

%N Number of n X 2 0..1 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A280227/b280227.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>7.

%F Empirical g.f.: x^2*(1 - x)*(1 + x)*(2 - x - 2*x^2 - x^3) / (1 - x - x^2)^2. - _Colin Barker_, Feb 13 2019

%e All solutions for n=4:

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

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

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

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

%Y Column 2 of A280233.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 29 2016