A280896 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 two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 9, 124, 1464, 15768, 159920, 1554304, 14632704, 134378112, 1209699584, 10713166848, 93585811456, 808068888576, 6907767091200, 58538748477440, 492296387559424, 4112143740076032, 34141836642680832, 281936660687224832

Offset

1,3

Links

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

Formula

Empirical: a(n) = 24*a(n-1) - 204*a(n-2) + 704*a(n-3) - 816*a(n-4) + 384*a(n-5) - 64*a(n-6) for n>8.

Empirical g.f.: x^2*(1 - 15*x + 112*x^2 - 380*x^3 + 408*x^4 - 192*x^5 + 32*x^6) / (1 - 8*x + 4*x^2)^3. - Colin Barker, Feb 14 2019

Example

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

Crossrefs

Column 2 of A280902.

Sequence in context: A269627 A209504 A320529 * A364940 A138438 A320646

Adjacent sequences: A280893 A280894 A280895 * A280897 A280898 A280899

Keyword

nonn

Author

R. H. Hardin, Jan 10 2017

Status

approved