A275178 Number of n X 3 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

5, 16, 25, 41, 85, 181, 389, 834, 1781, 3799, 8110, 17328, 37032, 79130, 169059, 361178, 771648, 1648657, 3522441, 7525825, 16079113, 34353402, 73396957, 156814715, 335039190, 715820740, 1529371036, 3267543982, 6981199507

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - a(n-4) - a(n-5) for n>8.

Empirical g.f.: x*(5 - 4*x - 9*x^2 + 12*x^3 - 4*x^4 - 17*x^5 + 11*x^6 + 5*x^7) / ((1 - x)*(1 - 3*x + 3*x^2 - 2*x^3 - x^4)). - Colin Barker, Feb 01 2019

Example

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

Crossrefs

Column 3 of A275183.

Sequence in context: A102045 A055508 A274356 * A171787 A227586 A335416

Adjacent sequences: A275175 A275176 A275177 * A275179 A275180 A275181

Keyword

nonn

Author

R. H. Hardin, Jul 19 2016

Status

approved