A280474 - OEIS

%I #8 Feb 13 2019 11:19:27

%S 1,6,30,158,846,4446,22734,113310,552654,2647390,12492366,58202526,

%T 268228430,1224529758,5544352206,24921415326,111297979854,

%U 494186360670,2182903872334,9596971862430,42012203555406,183197641092446

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

%H R. H. Hardin, <a href="/A280474/b280474.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 15*a(n-1) - 87*a(n-2) + 245*a(n-3) - 348*a(n-4) + 240*a(n-5) - 64*a(n-6).

%F Conjectures from _Colin Barker_, Feb 13 2019: (Start)

%F G.f.: x*(1 - 3*x)*(1 - 6*x + 9*x^2 + 12*x^3) / ((1 - x)^3*(1 - 4*x)^3).

%F a(n) = (8*(4^n-1) + 21*4^n*n + 6*(32+4^n)*n^2) / 324.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A280480.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 04 2017