A279460 Number of n X 2 0..1 arrays with no element equal 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, 2, 6, 20, 66, 210, 658, 2036, 6236, 18928, 57032, 170790, 508748, 1508462, 4454576, 13107640, 38446722, 112448726, 328044512, 954771282, 2772970950, 8038036642, 23258558892, 67190053760, 193807573324, 558249440024, 1605908314802

Offset

1,2

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) - 3*a(n-4) - 14*a(n-5) - 14*a(n-6) - 14*a(n-7) - 13*a(n-8) - 6*a(n-9) - a(n-10).

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

Example

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

Crossrefs

Column 2 of A279466.

Sequence in context: A148474 A156831 A027061 * A096487 A083323 A174846

Adjacent sequences: A279457 A279458 A279459 * A279461 A279462 A279463

Keyword

nonn

Author

R. H. Hardin, Dec 12 2016

Status

approved