A296719 Number of n X 2 0..1 arrays with each 1 adjacent to 0, 2 or 4 king-move neighboring 1s.

3, 9, 21, 57, 153, 393, 1041, 2745, 7185, 18921, 49761, 130713, 343761, 903753, 2375553, 6245625, 16419249, 43163817, 113476065, 298319193, 784254225, 2061749001, 5420172609, 14249195961, 37460035185, 98479462761, 258894708897

Offset

1,1

Links

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

Formula

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

Empirical g.f.: 3*x*(1 + 2*x + 2*x^2) / (1 - x - 2*x^2 - 6*x^3).

Example

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

Crossrefs

Column 2 of A296725.

Sequence in context: A345108 A007056 A026551 * A060578 A147078 A341704

Adjacent sequences: A296716 A296717 A296718 * A296720 A296721 A296722

Keyword

nonn

Author

R. H. Hardin, Dec 19 2017

Status

approved