A281321 Number of n X 3 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.

1, 46, 1266, 27144, 521848, 9439296, 164206368, 2780073856, 46137121152, 754039756800, 12175185631744, 194665401600000, 3087240149809152, 48627451780710400, 761481161055412224, 11864530809764020224

Offset

1,2

Links

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

Formula

Empirical: a(n) = 28*a(n-1) - 180*a(n-2) - 224*a(n-3) - 64*a(n-4) for n>5.

Empirical g.f.: x*(1 + 18*x + 158*x^2 + 200*x^3 + 64*x^4) / (1 - 14*x - 8*x^2)^2. - Colin Barker, Feb 18 2019

Example

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

Crossrefs

Column 3 of A281326.

Sequence in context: A333066 A261940 A060561 * A188412 A066403 A286788

Adjacent sequences: A281318 A281319 A281320 * A281322 A281323 A281324

Keyword

nonn

Author

R. H. Hardin, Jan 20 2017

Status

approved