A283197 Number of n X 2 0..1 arrays with no 1 equal to more than two of its horizontal and vertical neighbors, with the exception of exactly one element.

0, 0, 6, 36, 176, 824, 3668, 15808, 66640, 276184, 1129482, 4570084, 18329920, 72981648, 288779688, 1136580576, 4452663936, 17372989712, 67541322638, 261743811012, 1011439313456, 3898369209992, 14990343112316, 57519762677984

Offset

1,3

Comments

Column 2 of A283203.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 5*a(n-2) - 8*a(n-3) - 18*a(n-4) - 4*a(n-5) + 6*a(n-6) + 8*a(n-7) + 3*a(n-8) - 2*a(n-9) - a(n-10).

Empirical g.f.: 2*x^3*(1 + x)*(3 - 3*x - 2*x^2) / (1 - 3*x - 2*x^2 - 2*x^3 + x^4 + x^5)^2. - Colin Barker, Mar 22 2018

Example

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

Crossrefs

Cf. A283203.

Sequence in context: A132165 A200573 A224130 * A218265 A258629 A294465

Adjacent sequences: A283194 A283195 A283196 * A283198 A283199 A283200

Keyword

nonn

Author

R. H. Hardin, Mar 02 2017

Status

approved