A281394 Number of n X 2 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 6, 36, 160, 676, 2692, 10352, 38868, 143276, 520736, 1871380, 6663484, 23545568, 82661076, 288590204, 1002706896, 3469289876, 11959062188, 41088781264, 140757051348, 480912678028, 1639160372000, 5574818816340

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) - 6*a(n-3) - 5*a(n-4) + 12*a(n-5) + 4*a(n-6) - 4*a(n-8).

Empirical g.f.: 2*x^3*(1 + x - x^2)*(3 - 3*x - x^2) / (1 - 3*x - x^2 + 2*x^4)^2. - Colin Barker, Feb 18 2019

Example

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

Crossrefs

Column 2 of A281400.

Sequence in context: A223946 A223919 A263952 * A225380 A225012 A228458

Adjacent sequences: A281391 A281392 A281393 * A281395 A281396 A281397

Keyword

nonn

Author

R. H. Hardin, Jan 21 2017

Status

approved