A283727 Number of 2 X n 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

0, 0, 10, 60, 242, 1032, 4220, 16376, 62564, 235728, 875630, 3220084, 11746262, 42545240, 153181664, 548710320, 1956760904, 6950669984, 24604072658, 86824376236, 305540509370, 1072522794920, 3756266150212, 13128230615656

Offset

1,3

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 31*a(n-4) + 14*a(n-5) + 51*a(n-6) + 52*a(n-7) + 12*a(n-8) - 96*a(n-9) - 64*a(n-10).

Empirical g.f.: 2*x^3*(1 - 2*x)*(1 + 2*x)*(5 - 4*x^2) / ((1 + x + 2*x^2)^2*(1 - 4*x + x^2 + 4*x^3)^2). - Colin Barker, Feb 21 2019

Example

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

Crossrefs

Row 2 of A283726.

Sequence in context: A144560 A076160 A266732 * A349415 A228581 A241929

Adjacent sequences: A283724 A283725 A283726 * A283728 A283729 A283730

Keyword

nonn

Author

R. H. Hardin, Mar 15 2017

Status

approved