A281124 Number of n X 2 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 2, 28, 208, 1364, 8354, 48992, 278966, 1554744, 8524848, 46147848, 247246206, 1313446848, 6927856426, 36320588564, 189426835088, 983467437564, 5085683787674, 26206495324448, 134618732560222, 689572430485168

Offset

1,2

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 8*a(n-2) - 30*a(n-3) - 24*a(n-4) - 8*a(n-5) - a(n-6).

Empirical g.f.: 2*x^2*(1 + x)*(1 + 5*x - 5*x^2 - 3*x^3) / (1 - 4*x - 4*x^2 - x^3)^2. - Colin Barker, Feb 15 2019

Example

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

Crossrefs

Column 2 of A281129.

Sequence in context: A001798 A123787 A035601 * A244721 A001759 A243475

Adjacent sequences: A281121 A281122 A281123 * A281125 A281126 A281127

Keyword

nonn

Author

R. H. Hardin, Jan 15 2017

Status

approved