A296593 Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1, 2 or 3 neighboring 1s.

2, 11, 39, 136, 494, 1785, 6432, 23201, 83695, 301885, 1088905, 3927736, 14167501, 51102728, 184329596, 664884245, 2398264069, 8650634510, 31203185035, 112551137627, 405976459392, 1464373342374, 5282053272285, 19052577620620

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) + 4*a(n-3) + a(n-4) + a(n-6) - a(n-7) - a(n-8).

Empirical g.f.: x*(2 + 5*x + 4*x^2 + x^4 - 2*x^6 - x^7) / (1 - 3*x - x^2 - 4*x^3 - x^4 - x^6 + x^7 + x^8). - Colin Barker, Feb 23 2019

Example

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

Crossrefs

Column 2 of A296599.

Sequence in context: A000175 A276659 A187259 * A125064 A361493 A274326

Adjacent sequences: A296590 A296591 A296592 * A296594 A296595 A296596

Keyword

nonn

Author

R. H. Hardin, Dec 16 2017

Status

approved