A231356 Number of (n+1) X (1+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..3 introduced in row major order.

1, 2, 4, 12, 33, 102, 329, 1075, 3622, 12298, 42132, 145145, 501380, 1735895, 6017101, 20873202, 72444888, 251507292, 873325097, 3032847106, 10533086197, 36583055791, 127062078054, 441325714766, 1532875934756, 5324239108913

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) - 5*a(n-3) - 24*a(n-4) - 2*a(n-5) + 15*a(n-6) + 9*a(n-7).

Empirical g.f.: x*(1 - x - 7*x^2 - 5*x^3 + 11*x^4 + 13*x^5 + 3*x^6) / ((1 - x)*(1 - x - 2*x^2 - x^3)*(1 - x - 6*x^2 - 9*x^3)). - Colin Barker, Sep 28 2018

Example

Some solutions for n=7:
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..1....0..1....0..0....0..0....0..1....0..1....0..1....0..1....0..0....0..1
..1..1....1..1....1..1....0..1....1..1....1..1....1..1....1..1....0..0....1..1
..1..2....2..2....1..1....1..1....1..2....2..2....0..0....1..1....0..0....1..1
..2..2....2..1....1..1....1..2....2..2....2..2....0..0....1..1....0..0....2..2
..3..3....1..1....1..1....2..2....0..0....0..0....0..0....2..2....0..0....2..1
..3..2....1..3....1..1....0..0....0..1....0..0....1..1....2..1....1..1....1..1
..2..2....3..3....1..1....0..0....1..1....0..0....1..1....1..1....1..1....1..1

Crossrefs

Column 1 of A231363.

Sequence in context: A148195 A169807 A005028 * A148196 A148197 A148198

Adjacent sequences: A231353 A231354 A231355 * A231357 A231358 A231359

Keyword

nonn

Author

R. H. Hardin, Nov 08 2013

Status

approved