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

1,3

Links

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

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)

Example

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

Crossrefs

Column 2 of A277767.

Sequence in context: A356373 A137482 A346033 * A203576 A178605 A212895

Adjacent sequences: A277758 A277759 A277760 * A277762 A277763 A277764

Keyword

nonn

Author

R. H. Hardin, Oct 29 2016

Status

approved