A274853 Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,0) (0,-1) or (-2,-2) and new values introduced in order 0..2.

2, 9, 19, 43, 100, 233, 542, 1260, 2929, 6809, 15829, 36798, 85545, 198868, 462312, 1074745, 2498479, 5808259, 13502564, 31389653, 72972090, 169639528, 394364057, 916785205, 2131267029, 4954594734, 11518035349, 26776183608, 62247074860

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n>4.

Empirical g.f.: x*(2 + 3*x - 4*x^2 + 2*x^3) / (1 - 3*x + 2*x^2 - x^3). - Colin Barker, Jan 31 2019

Example

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

Crossrefs

Column 3 of A274858.

Sequence in context: A173663 A294546 A135207 * A264670 A026541 A038249

Adjacent sequences: A274850 A274851 A274852 * A274854 A274855 A274856

Keyword

nonn

Author

R. H. Hardin, Jul 09 2016

Status

approved