A278088 Number of n X 2 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

0, 2, 3, 10, 27, 76, 214, 599, 1683, 4721, 13250, 37183, 104346, 292828, 821761, 2306111, 6471639, 18161366, 50966255, 143026636, 401375754, 1126381063, 3160963987, 8870615501, 24893614638, 69858968603, 196045273658, 550161991984

Offset

1,2

Links

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

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) + 3*a(n-3) for n>5.

Empirical g.f.: x^2*(2 + x - x^2 - x^3) / (1 - x - 4*x^2 - 3*x^3). - Colin Barker, Feb 07 2019

Example

All solutions for n=4:
..0..1. .0..0. .0..0. .0..1. .0..1. .0..1. .0..0. .0..1. .0..0. .0..0
..0..1. .1..1. .1..1. .0..1. .0..1. .0..1. .1..1. .0..1. .1..1. .1..1
..1..1. .0..1. .1..0. .0..1. .0..1. .0..0. .1..1. .1..0. .0..0. .0..1
..0..0. .0..0. .1..0. .0..1. .0..0. .1..1. .0..0. .1..0. .1..1. .0..1

Crossrefs

Column 2 of A278094.

Sequence in context: A211208 A303836 A238937 * A052929 A151415 A134588

Adjacent sequences: A278085 A278086 A278087 * A278089 A278090 A278091

Keyword

nonn

Author

R. H. Hardin, Nov 11 2016

Status

approved