A279378 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with new values introduced in order 0 sequentially upwards.

1, 3, 8, 22, 61, 170, 472, 1310, 3637, 10099, 28041, 77857, 216174, 600221, 1666552, 4627285, 12847943, 35673112, 99048614, 275014633, 763595218, 2120169576, 5886782590, 16345017705, 45382957439, 126008601709, 349870713613

Offset

1,2

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) + 3*a(n-4) + a(n-5).

Empirical g.f.: x*(1 + x)*(1 + x^2) / (1 - 2*x - x^2 - 2*x^3 - 3*x^4 - x^5). - Colin Barker, Feb 10 2019

Example

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

Crossrefs

Column 2 of A279384.

Sequence in context: A318862 A318820 A200752 * A048579 A121449 A025566

Adjacent sequences: A279375 A279376 A279377 * A279379 A279380 A279381

Keyword

nonn

Author

R. H. Hardin, Dec 11 2016

Status

approved