A279852 - OEIS

%I #7 Feb 11 2019 14:20:43

%S 2,10,49,168,557,1758,5441,16500,49253,145290,424425,1229824,3539405,

%T 10127350,28832593,81728396,230776757,649427170,1821994809,5097729560,

%U 14227693853,39620451150,110107647905,305424435364,845754303493

%N Number of n X 3 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A279852/b279852.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 9*a(n-4) - 4*a(n-5) - 4*a(n-6) for n>9.

%F Empirical g.f.: x*(2 + 2*x + 13*x^2 - 8*x^3 + x^4 - 36*x^5 + 12*x^6 + 16*x^8) / (1 - 2*x - x^2 - 2*x^3)^2. - _Colin Barker_, Feb 11 2019

%e Some solutions for n=4:

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

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

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

%e ..2..2..1. .1..0..1. .0..0..0. .0..0..1. .1..0..0. .0..2..0. .2..2..2

%Y Column 3 of A279856.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2016