A277761 Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

0, 1, 2, 14, 56, 284, 1304, 6248, 29408, 139472, 659360, 3121376, 14768000, 69887936, 330703232, 1564924544, 7405262336, 35042157824, 165821110784, 784674242048, 3713117739008, 17570663078912, 83145267845120, 393447636985856

Offset: 1

Author

R. H. Hardin, Oct 29 2016

Keywords

• nonn

Examples

			Some solutions for n=4:
..0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..1
..2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2. .2..2
..2..0. .0..1. .1..2. .0..1. .1..0. .0..1. .0..1. .2..1. .1..0. .1..0
..1..1. .2..2. .0..0. .2..0. .0..2. .1..2. .2..1. .0..0. .1..2. .2..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 2 of A277767.

Formula

Empirical: a(n) = 4*a(n-1) + 6*a(n-2) - 12*a(n-3).

Conjectures from Colin Barker, Feb 05 2019: (Start)

G.f.: x^2*(1 - 2*x) / ((1 + 2*x)*(1 - 6*x + 6*x^2)).

a(n) = (3*(-1)^n*2^(2+n) - (-5+sqrt(3))*(3+sqrt(3))^n + (3-sqrt(3))^n*(5+sqrt(3))) / 132.

(End)