A279162 - OEIS

%I #9 Feb 10 2019 09:01:28

%S 1,0,0,8,24,88,284,772,2000,5008,12060,28300,65192,147736,330340,

%T 730740,1601744,3483616,7526252,16167132,34555192,73534440,155880628,

%U 329312132,693584736,1456820784,3052436156,6381514348,13314563144,27728987832

%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 two elements, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A279162/b279162.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 19*a(n-2) + 31*a(n-3) - 52*a(n-4) + 82*a(n-5) - 84*a(n-6) + 84*a(n-7) - 96*a(n-8) + 56*a(n-9) - 32*a(n-10) + 32*a(n-11).

%F Empirical g.f.: x*(1 - 7*x + 19*x^2 - 23*x^3 + 20*x^4 - 10*x^5 - 40*x^6 + 44*x^7 - 48*x^8 + 96*x^9) / ((1 - 2*x)^2*(1 - x - 2*x^3)^3). - _Colin Barker_, Feb 10 2019

%e All solutions for n=4:

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

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

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

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

%Y Column 2 of A279168.

%K nonn

%O 1,4

%A _R. H. Hardin_, Dec 07 2016