A279736 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

2, 6, 35, 168, 766, 3402, 14827, 63680, 270313, 1136546, 4740986, 19644984, 80939021, 331835984, 1354628539, 5508982340, 22328647462, 90229615030, 363633214831, 1461903606752, 5864244756909, 23476219277174, 93808204087890

Offset

1,1

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 54*a(n-3) - 45*a(n-4) + 20*a(n-5) - 4*a(n-6) for n>7.

Empirical g.f.: x*(1 - x)*(1 - 2*x)*(2 - 8*x + 17*x^2 - 13*x^3 + 4*x^4) / (1 - 5*x + 5*x^2 - 2*x^3)^2. - Colin Barker, Feb 11 2019

Example

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

Crossrefs

Column 3 of A279741.

Sequence in context: A101262 A135965 A018983 * A081003 A038181 A305275

Adjacent sequences: A279733 A279734 A279735 * A279737 A279738 A279739

Keyword

nonn

Author

R. H. Hardin, Dec 18 2016

Status

approved