A296645 Number of n X 2 0..1 arrays with each 1 adjacent to 0, 1 or 3 king-move neighboring 1s.

4, 12, 29, 85, 248, 664, 1897, 5385, 14924, 42180, 118869, 332765, 937088, 2635856, 7400673, 20815825, 58523540, 164457532, 462389261, 1299858917, 3653657736, 10271361928, 28873923801, 81164992281, 228166526044, 641398040884

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) + 9*a(n-3) - 4*a(n-4) - 12*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(4 + 8*x + 5*x^2 - 16*x^3 - 16*x^4 - 4*x^5) / (1 - x - 3*x^2 - 9*x^3 + 4*x^4 + 12*x^5 + 4*x^6). - Colin Barker, Feb 23 2019

Example

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

Crossrefs

Column 2 of A296651.

Sequence in context: A036889 A036895 A309297 * A280007 A061726 A067706

Adjacent sequences: A296642 A296643 A296644 * A296646 A296647 A296648

Keyword

nonn

Author

R. H. Hardin, Dec 17 2017

Status

approved