A296682 Number of n X 2 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s.

2, 12, 43, 145, 524, 1888, 6737, 24093, 86250, 308600, 1104107, 3950629, 14135676, 50578004, 180970841, 647524153, 2316876914, 8289912724, 29661766587, 106131439497, 379744147900, 1358745529912, 4861666537265, 17395311311589

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) + 11*a(n-3) - 2*a(n-4) + 8*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(2 + 6*x + 9*x^2 + 6*x^3 + 4*x^4 - 4*x^5) / (1 - 3*x + x^2 - 11*x^3 + 2*x^4 - 8*x^5 + 4*x^6). - Colin Barker, Feb 24 2019

Example

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

Crossrefs

Column 2 of A296688.

Sequence in context: A189491 A301556 A055681 * A351616 A111389 A203278

Adjacent sequences: A296679 A296680 A296681 * A296683 A296684 A296685

Keyword

nonn

Author

R. H. Hardin, Dec 18 2017

Status

approved