A297088 Number of n X 2 0..1 arrays with no 1 adjacent to 3 king-move neighboring 1s.

4, 15, 45, 152, 511, 1681, 5588, 18575, 61621, 204608, 679407, 2255577, 7488924, 24864735, 82554557, 274095080, 910042783, 3021494049, 10031871012, 33307511407, 110586567109, 367166113104, 1219053634447, 4047464337257

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) + 3*a(n-3) - 14*a(n-4) + 4*a(n-5).

Empirical g.f.: x*(4 - x - 7*x^2 - 10*x^3 + 4*x^4) / (1 - 4*x + 2*x^2 - 3*x^3 + 14*x^4 - 4*x^5). - Colin Barker, Feb 26 2019

Example

Some solutions for n=7:
..1..0. .1..1. .1..0. .0..1. .1..1. .0..0. .0..1. .0..1. .1..0. .0..0
..0..0. .0..1. .0..0. .0..0. .0..0. .0..1. .1..0. .1..0. .1..0. .1..0
..0..0. .1..1. .1..1. .0..1. .1..0. .1..1. .0..0. .0..0. .0..0. .0..0
..1..0. .1..1. .0..0. .0..0. .0..0. .0..0. .1..0. .1..0. .1..0. .0..1
..0..1. .1..1. .0..1. .1..0. .0..0. .1..0. .1..0. .1..0. .0..0. .0..0
..1..0. .0..1. .1..1. .1..0. .1..0. .0..0. .0..0. .0..0. .0..1. .0..1
..1..0. .0..0. .0..0. .0..0. .0..0. .1..0. .1..0. .0..0. .1..1. .1..1

Crossrefs

Column 2 of A297094.

Sequence in context: A075673 A062827 A074448 * A152116 A195688 A111038

Adjacent sequences: A297085 A297086 A297087 * A297089 A297090 A297091

Keyword

nonn

Author

R. H. Hardin, Dec 25 2017

Status

approved