A296968 Number of n X 2 0..1 arrays with each 1 adjacent to 2, 4 or 5 king-move neighboring 1s.

1, 5, 11, 21, 59, 145, 323, 793, 1939, 4561, 10939, 26425, 63107, 151057, 362923, 869609, 2083059, 4996033, 11977083, 28703897, 68813891, 164968369, 395429963, 947913481, 2272359443, 5447139489, 13057617307, 31301457785, 75034524387

Offset

1,2

Links

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

Formula

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

Empirical g.f.: x*(1 + 3*x + 2*x^2 - 2*x^3 + 2*x^4) / (1 - 2*x + x^2 - 6*x^3 + 4*x^4 - 2*x^5). - Colin Barker, Feb 25 2019

Example

Some solutions for n=5:
..0..0. .0..0. .0..0. .1..1. .1..0. .0..0. .0..0. .1..0. .0..0. .1..1
..0..0. .0..1. .0..0. .0..1. .1..1. .1..1. .0..0. .1..1. .0..0. .0..1
..0..0. .1..1. .1..1. .0..0. .0..0. .1..0. .1..1. .1..1. .1..0. .0..0
..1..1. .0..0. .1..0. .1..1. .1..1. .0..0. .0..1. .1..1. .1..1. .1..0
..1..0. .0..0. .0..0. .0..1. .1..0. .0..0. .1..1. .1..0. .0..0. .1..1

Crossrefs

Column 2 of A296974.

Sequence in context: A234597 A261982 A296033 * A184552 A069097 A222548

Adjacent sequences: A296965 A296966 A296967 * A296969 A296970 A296971

Keyword

nonn

Author

R. H. Hardin, Dec 22 2017

Status

approved