A279852 Number of n X 3 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

2, 10, 49, 168, 557, 1758, 5441, 16500, 49253, 145290, 424425, 1229824, 3539405, 10127350, 28832593, 81728396, 230776757, 649427170, 1821994809, 5097729560, 14227693853, 39620451150, 110107647905, 305424435364, 845754303493

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 9*a(n-4) - 4*a(n-5) - 4*a(n-6) for n>9.

Empirical g.f.: x*(2 + 2*x + 13*x^2 - 8*x^3 + x^4 - 36*x^5 + 12*x^6 + 16*x^8) / (1 - 2*x - x^2 - 2*x^3)^2. - Colin Barker, Feb 11 2019

Example

Some solutions for n=4:
..0..0..0. .0..0..0. .0..1..1. .0..1..1. .0..0..0. .0..1..1. .0..0..1
..1..1..1. .1..1..1. .1..1..1. .0..1..1. .0..0..0. .0..1..1. .1..1..1
..1..1..1. .1..1..1. .1..1..1. .0..1..1. .1..0..0. .0..0..0. .1..1..1
..2..2..1. .1..0..1. .0..0..0. .0..0..1. .1..0..0. .0..2..0. .2..2..2

Crossrefs

Column 3 of A279856.

Sequence in context: A270664 A330543 A052576 * A219662 A355153 A268108

Adjacent sequences: A279849 A279850 A279851 * A279853 A279854 A279855

Keyword

nonn

Author

R. H. Hardin, Dec 20 2016

Status

approved