A282125 Number of n X 2 0..2 arrays with no element unequal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 30, 412, 4018, 35472, 296062, 2378276, 18602538, 142686584, 1078094998, 8049085452, 59514821186, 436531302624, 3180302488110, 23036382105332, 166033195371866, 1191480270802248, 8517590180994246, 60683797705011932

Offset

1,3

Links

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

Formula

Empirical: a(n) = 14*a(n-1) - 57*a(n-2) + 88*a(n-3) - 256*a(n-4) + 240*a(n-5) - 320*a(n-6) + 256*a(n-7) - 64*a(n-8).

Empirical g.f.: 2*x^3*(3 - 2*x + 4*x^2)*(5 + 2*x - 12*x^2) / (1 - 7*x + 4*x^2 - 16*x^3 + 8*x^4)^2. - Colin Barker, Feb 20 2019

Example

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

Crossrefs

Column 2 of A282130.

Sequence in context: A010835 A022722 A278016 * A296917 A255002 A126922

Adjacent sequences: A282122 A282123 A282124 * A282126 A282127 A282128

Keyword

nonn

Author

R. H. Hardin, Feb 06 2017

Status

approved