A295979 Number of n X 2 0..1 arrays with each 1 adjacent to 2 or 3 king-move neighboring 1s.

1, 6, 15, 28, 90, 281, 737, 2095, 6268, 17965, 51360, 149540, 433577, 1250789, 3620541, 10489538, 30345263, 87801224, 254176114, 735652561, 2128923525, 6161699035, 17833776016, 51613806741, 149380609556, 432342904636

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 9*a(n-3) - 10*a(n-4) - 4*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(1 + 3*x - x^2 - 14*x^3 - 8*x^4 - 4*x^5) / (1 - 3*x + 2*x^2 - 9*x^3 + 10*x^4 + 4*x^5 + 4*x^6). - Colin Barker, Feb 22 2019

Example

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

Crossrefs

Column 2 of A295985.

Sequence in context: A144519 A066995 A263896 * A338488 A365418 A180953

Adjacent sequences: A295976 A295977 A295978 * A295980 A295981 A295982

Keyword

nonn

Author

R. H. Hardin, Dec 01 2017

Status

approved