A281074 Number of n X 2 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 6, 24, 92, 318, 1056, 3406, 10770, 33542, 103226, 314634, 951396, 2857604, 8534022, 25360354, 75037878, 221184144, 649773710, 1903099818, 5558851080, 16197428578, 47091498180, 136634149236, 395704051072, 1144040493756

Offset

1,3

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 8*a(n-3) - 5*a(n-4) - 8*a(n-5) + 11*a(n-6) + a(n-8) + 6*a(n-9) - 2*a(n-10) - 4*a(n-11) - a(n-12).

Empirical g.f.: 2*x^3*(3 - 6*x + 7*x^2 - 9*x^3 - x^4 - 4*x^6 + x^7 + x^8) / ((1 - x)^2*(1 - 2*x - x^2 - 2*x^3 - 3*x^4 - x^5)^2). - Colin Barker, Feb 15 2019

Example

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

Crossrefs

Column 2 of A281080.

Sequence in context: A365978 A079839 A270955 * A255296 A242432 A255476

Adjacent sequences: A281071 A281072 A281073 * A281075 A281076 A281077

Keyword

nonn

Author

R. H. Hardin, Jan 14 2017

Status

approved