A280155 Number of n X 2 0..1 arrays with no element unequal to a strict majority 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, 4, 8, 18, 40, 92, 208, 470, 1060, 2384, 5352, 11992, 26824, 59906, 133592, 297510, 661720, 1470062, 3262264, 7231940, 16016596, 35439722, 78349800, 173074816, 382029988, 842648168, 1857362384, 4091321478, 9006604780, 19815365450

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) for n>8.

Empirical g.f.: 2*x^2*(2 - 5*x^2 - 6*x^3 - x^4 + 2*x^5 + x^6) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Feb 13 2019

Example

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

Crossrefs

Column 2 of A280161.

Sequence in context: A228231 A175657 A080287 * A075310 A075797 A351323

Adjacent sequences: A280152 A280153 A280154 * A280156 A280157 A280158

Keyword

nonn

Author

R. H. Hardin, Dec 27 2016

Status

approved