A275505 Number of 5 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,-1) and new values introduced in order 0..2.

12, 56, 232, 988, 4180, 17712, 75024, 317812, 1346268, 5702888, 24157816, 102334156, 433494436, 1836311904, 7778742048, 32951280100, 139583862444, 591286729880, 2504730781960, 10610209857724, 44945570212852

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3).

Conjectures from Colin Barker, Feb 04 2019: (Start)

G.f.: 4*x*(3 + 5*x + x^2) / ((1 + x)*(1 - 4*x - x^2)).

a(n) = (10*(-1)^n + (15-7*sqrt(5))*(2-sqrt(5))^n + (2+sqrt(5))^n*(15+7*sqrt(5))) / 10.

(End)

Example

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

Crossrefs

Row 5 of A275504.

Sequence in context: A009430 A348584 A035289 * A009827 A068418 A068414

Adjacent sequences: A275502 A275503 A275504 * A275506 A275507 A275508

Keyword

nonn

Author

R. H. Hardin, Jul 30 2016

Status

approved