A297067 Number of n X 2 0..1 arrays with no 1 adjacent to 1 king-move neighboring 1.

3, 10, 32, 103, 350, 1201, 4143, 14353, 49844, 173276, 602727, 2097232, 7298725, 25403085, 88419267, 307764514, 1071262948, 3728865871, 12979534274, 45179596085, 157262816291, 547406567737, 1905434794508, 6632515135472

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - a(n-2) - a(n-3) - 4*a(n-4) - 8*a(n-5).

Empirical g.f.: x*(3 - 2*x - 5*x^2 - 12*x^3 - 8*x^4) / (1 - 4*x + x^2 + x^3 + 4*x^4 + 8*x^5). - Colin Barker, Feb 25 2019

Example

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

Crossrefs

Column 2 of A297073.

Sequence in context: A292398 A273351 A033505 * A063782 A071718 A261058

Adjacent sequences: A297064 A297065 A297066 * A297068 A297069 A297070

Keyword

nonn

Author

R. H. Hardin, Dec 24 2017

Status

approved