A275229 Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

2, 11, 61, 339, 1885, 10483, 58301, 324243, 1803293, 10029107, 55777405, 310208979, 1725243613, 9595033459, 53363285309, 296782729491, 1650572823965, 9179747931827, 51053652931069, 283937587062867, 1579133885991517

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 8*a(n-2).

Conjectures from Colin Barker, Feb 02 2019: (Start)

G.f.: x*(2 - 3*x) / (1 - 7*x + 8*x^2).

a(n) = (2^(-4-n) * ((7-sqrt(17))^n * (-11+3*sqrt(17)) + (7+sqrt(17))^n*(11+3*sqrt(17)))) / sqrt(17).

(End)

Example

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

Crossrefs

Row 3 of A275228.

Sequence in context: A240548 A255549 A352311 * A074615 A126034 A308729

Adjacent sequences: A275226 A275227 A275228 * A275230 A275231 A275232

Keyword

nonn

Author

R. H. Hardin, Jul 20 2016

Status

approved