A281133 Number of n X 2 0..2 arrays with no element equal to more than one of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 24, 112, 504, 2528, 11712, 52160, 230048, 1000320, 4294016, 18264832, 77098880, 323290624, 1347997696, 5593390080, 23110676992, 95130810368, 390287108096, 1596449140736, 6512744568832, 26504685772800, 107628465111040

Offset

1,3

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 32*a(n-3) - 84*a(n-4) + 96*a(n-5) - 96*a(n-6) + 128*a(n-7) - 64*a(n-8).

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

Example

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

Crossrefs

Column 2 of A281139.

Sequence in context: A162451 A307859 A263542 * A064595 A064591 A228433

Adjacent sequences: A281130 A281131 A281132 * A281134 A281135 A281136

Keyword

nonn

Author

R. H. Hardin, Jan 15 2017

Status

approved