A275126 Number of n X 3 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

5, 16, 45, 129, 373, 1083, 3148, 9157, 26623, 77372, 224857, 653525, 1899462, 5520787, 16046124, 46637722, 135551305, 393976458, 1145083415, 3328158969, 9673218248, 28114986916, 81715561920, 237504397813, 690301064559

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) + 4*a(n-3) + a(n-4) + 3*a(n-5) + 8*a(n-6) + a(n-7) - 3*a(n-8) - a(n-9) for n>10.

Empirical g.f.: x*(5 + x + 7*x^2 + 6*x^3 + 7*x^4 + 11*x^5 - 4*x^6 - 10*x^7 - 5*x^8 - x^9) / (1 - 3*x + 2*x^2 - 4*x^3 - x^4 - 3*x^5 - 8*x^6 - x^7 + 3*x^8 + x^9). - Colin Barker, Jan 31 2019

Example

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

Crossrefs

Column 3 of A275131.

Sequence in context: A099327 A004146 A369803 * A071101 A110580 A351283

Adjacent sequences: A275123 A275124 A275125 * A275127 A275128 A275129

Keyword

nonn

Author

R. H. Hardin, Jul 17 2016

Status

approved