A279152 - OEIS

A279152

Number of n X 2 0..1 arrays with no element equal 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.

%I #8 Feb 10 2019 08:53:07

%S 0,0,4,12,30,72,162,356,766,1616,3378,7004,14406,29480,60090,122036,

%T 247150,499456,1007458,2029068,4081686,8202456,16469642,33046628,

%U 66271166,132836784,266160818,533127612,1067587174,2137374088,4278378970

%N Number of n X 2 0..1 arrays with no element equal 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="/A279152/b279152.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 6*a(n-3) - 12*a(n-4) + 8*a(n-5) - 4*a(n-6) + 8*a(n-7).

%F Empirical g.f.: 2*x^3*(2 - 2*x + x^2 - 6*x^3) / ((1 - 2*x)*(1 - x - 2*x^3)^2). - _Colin Barker_, Feb 10 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A279158.

%K nonn

%O 1,3

%A _R. H. Hardin_, Dec 06 2016