A268783 Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

1, 5, 17, 48, 131, 338, 850, 2091, 5061, 12095, 28608, 67095, 156244, 361652, 832757, 1908885, 4358285, 9915728, 22489147, 50862918, 114743814, 258261695, 580072917, 1300393467, 2910078592, 6501783407, 14504787560, 32313853992, 71896385513

Offset

1,2

Links

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

Formula

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

Empirical g.f.: x*(1 + 3*x + 4*x^2 + x^3) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Jan 15 2019

Example

Some solutions for n=4:
..1..0. .1..1. .0..0. .0..0. .0..0. .1..1. .0..0. .1..0. .0..0. .0..0
..0..0. .0..0. .1..0. .1..1. .0..0. .0..0. .1..1. .1..0. .1..0. .0..1
..0..1. .0..0. .1..0. .0..0. .1..1. .1..0. .0..0. .0..0. .0..1. .0..1
..1..0. .0..1. .0..1. .1..0. .0..0. .0..1. .0..0. .0..1. .1..0. .0..0

Crossrefs

Column 2 of A268789.

Sequence in context: A213767 A320854 A136303 * A273384 A006457 A115981

Adjacent sequences: A268780 A268781 A268782 * A268784 A268785 A268786

Keyword

nonn

Author

R. H. Hardin, Feb 13 2016

Status

approved