A280228 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

2, 6, 9, 16, 29, 52, 95, 168, 298, 522, 911, 1580, 2729, 4694, 8046, 13748, 23425, 39812, 67507, 114228, 192914, 325230, 547411, 919996, 1544029, 2588002, 4332630, 7245208, 12103013, 20197972, 33675911, 56098560, 93374074, 155296914

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>7.

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

Example

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

Crossrefs

Column 3 of A280233.

Sequence in context: A043548 A347535 A354975 * A254057 A257083 A054974

Adjacent sequences: A280225 A280226 A280227 * A280229 A280230 A280231

Keyword

nonn

Author

R. H. Hardin, Dec 29 2016

Status

approved