A279865 - OEIS

%I #9 Feb 26 2018 09:15:17

%S 0,1,0,6,6,30,54,158,342,846,1910,4446,10038,22734,50838,113310,

%T 250774,552654,1211958,2647390,5760630,12492366,27003990,58202526,

%U 125104086,268228430,573739254,1224529758,2608132022,5544352206,11764763670

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

%C Column 1 of A279871.

%H R. H. Hardin, <a href="/A279865/b279865.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +3*a(n-2) -11*a(n-3) -6*a(n-4) +12*a(n-5) +8*a(n-6).

%F Conjectures from _Colin Barker_, Feb 26 2018: (Start)

%F G.f.: x^2*(1 - x)^3 / ((1 + x)^3*(1 - 2*x)^3).

%F a(n) = (3*2^n*n^2 + 96*n^2 + 21*2^n*n + 2^(n+4) - 16) / 648 for n even.

%F a(n) = (3*2^n*n^2 - 96*n^2 + 21*2^n*n + 2^(n+4) + 16) / 648 for n odd.

%F (End)

%e All solutions for n=4:

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

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

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

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

%Y Cf. A279871.

%K nonn

%O 1,4

%A _R. H. Hardin_, Dec 21 2016