A280227 Number of n X 2 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.

0, 4, 6, 8, 14, 24, 42, 72, 124, 212, 362, 616, 1046, 1772, 2996, 5056, 8518, 14328, 24066, 40368, 67628, 113164, 189154, 315848, 526894, 878164, 1462372, 2433272, 4045694, 6721752, 11160282, 18517656, 30706396, 50888132, 84287066, 139531816

Offset

1,2

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*(1 - x)*(1 + x)*(2 - x - 2*x^2 - x^3) / (1 - x - x^2)^2. - Colin Barker, Feb 13 2019

Example

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

Crossrefs

Column 2 of A280233.

Sequence in context: A116897 A293763 A246324 * A181978 A302636 A000937

Adjacent sequences: A280224 A280225 A280226 * A280228 A280229 A280230

Keyword

nonn

Author

R. H. Hardin, Dec 29 2016

Status

approved