A279866 Number of n X 2 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

1, 4, 33, 96, 255, 610, 1437, 3292, 7451, 16662, 36921, 81200, 177399, 385450, 833365, 1794180, 3848019, 8225214, 17528049, 37250392, 78966831, 167021394, 352528653, 742650796, 1561730955, 3278806630, 6873273257, 14387809152, 30078027111

Offset

1,2

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 4*a(n-2) - 14*a(n-3) + 19*a(n-4) + 13*a(n-5) - 22*a(n-6) - 4*a(n-7) + 8*a(n-8) for n>9.

Empirical g.f.: x*(1 - x + 17*x^2 - 39*x^3 - 56*x^4 + 92*x^5 + 94*x^6 - 44*x^7 - 80*x^8) / ((1 - x)^2*(1 + x)^3*(1 - 2*x)^3). - Colin Barker, Feb 12 2019

Example

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

Crossrefs

Column 2 of A279871.

Sequence in context: A042831 A092207 A133630 * A066645 A295939 A297515

Adjacent sequences: A279863 A279864 A279865 * A279867 A279868 A279869

Keyword

nonn

Author

R. H. Hardin, Dec 21 2016

Status

approved