A295841 Number of n X 2 0..1 arrays with each 1 adjacent to 1 or 2 king-move neighboring 1s.

2, 11, 29, 80, 261, 789, 2354, 7199, 21889, 66280, 201313, 611401, 1855458, 5632611, 17100277, 51909760, 157581005, 478374029, 1452197426, 4408426199, 13382677305, 40625798040, 123327694601, 374385940001, 1136523495202, 3450144328891

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) + 6*a(n-3) - 8*a(n-4).

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

Example

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

Crossrefs

Column 2 of A295847.

Sequence in context: A009312 A154251 A092275 * A086252 A106926 A220095

Adjacent sequences: A295838 A295839 A295840 * A295842 A295843 A295844

Keyword

nonn

Author

R. H. Hardin, Nov 29 2017

Status

approved