A278171 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) (1,-1) or (1,0), with upper left element zero.

0, 2, 5, 13, 43, 137, 436, 1394, 4458, 14258, 45607, 145888, 466673, 1492823, 4775347, 15275728, 48865129, 156313412, 500027005, 1599523726, 5116675993, 16367605483, 52357919474, 167486425305, 535768092953, 1713855012003, 5482407483581

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) - 3*a(n-4) - 2*a(n-5) - a(n-6) for n>7.

Empirical g.f.: x^2*(1 + x)*(2 - 3*x - x^2 + x^4) / (1 - 3*x - x^2 + 3*x^4 + 2*x^5 + x^6). - Colin Barker, Feb 08 2019

Example

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

Crossrefs

Column 2 of A278177.

Sequence in context: A192745 A299430 A307263 * A212824 A338660 A286949

Adjacent sequences: A278168 A278169 A278170 * A278172 A278173 A278174

Keyword

nonn

Author

R. H. Hardin, Nov 13 2016

Status

approved