A281320 Number of n X 2 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 2, 28, 304, 2976, 27488, 244544, 2119168, 18011136, 150809088, 1247857664, 10226274304, 83138240512, 671370043392, 5390483210240, 43066315243520, 342583723687936, 2714813886234624, 21440990518444032, 168825545758343168

Offset

1,2

Links

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

Formula

Empirical: a(n) = 16*a(n-1) - 72*a(n-2) + 64*a(n-3) - 16*a(n-4).

Empirical g.f.: 2*x^2*(1 - 2*x) / (1 - 8*x + 4*x^2)^2. - Colin Barker, Feb 18 2019

Example

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

Crossrefs

Column 2 of A281326.

Sequence in context: A230589 A097353 A092801 * A152280 A061629 A230130

Adjacent sequences: A281317 A281318 A281319 * A281321 A281322 A281323

Keyword

nonn

Author

R. H. Hardin, Jan 20 2017

Status

approved