A296733 Number of n X 2 0..1 arrays with each 1 adjacent to 1, 2 or 4 king-move neighboring 1s.

2, 11, 31, 88, 287, 881, 2686, 8347, 25763, 79376, 245227, 757045, 2336222, 7212287, 22263871, 68722504, 212138639, 654844841, 2021399374, 6239772643, 19261292171, 59456768000, 183534426499, 566544237805, 1748839677662, 5398414303799

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) + 8*a(n-3) - 12*a(n-4) + 2*a(n-5) - 12*a(n-6).

Empirical g.f.: x*(2 + x + 2*x^2)*(1 + 2*x - 2*x^2 - 6*x^3) / (1 - 3*x + x^2 - 8*x^3 + 12*x^4 - 2*x^5 + 12*x^6). - Colin Barker, Feb 25 2019

Example

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

Crossrefs

Column 2 of A296739.

Sequence in context: A121346 A106847 A092761 * A087933 A190259 A190261

Adjacent sequences: A296730 A296731 A296732 * A296734 A296735 A296736

Keyword

nonn

Author

R. H. Hardin, Dec 19 2017

Status

approved