A214160 Number of 0..5 colorings of an n X 3 array circular in the 3 direction with new values 0..5 introduced in row major order.

1, 18, 902, 60320, 4242606, 300785428, 21350933122, 1515863103360, 107625695720486, 7641417965382188, 542540604803692842, 38520382162939430200, 2734947125009349378766, 194181245781510954496548

Offset

1,2

Comments

Column 2 of A214166.

Links

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

Formula

Empirical: a(n) = 84*a(n-1) - 945*a(n-2) + 1562*a(n-3).

Conjectures from Colin Barker, Jul 22 2018: (Start)

G.f.: x*(1 - 66*x + 335*x^2) / ((1 - 2*x)*(1 - 11*x)*(1 - 71*x)).

a(n) = (781*2^n + 213*11^n + 11*71^n)/4686.

(End)

Example

Some solutions for n=4:
..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2
..1..0..3....1..2..3....2..0..1....1..0..3....2..3..0....2..0..1....2..3..0
..2..3..0....3..4..5....0..2..3....2..3..4....3..2..4....0..1..2....3..4..1
..4..2..3....4..0..1....1..0..4....3..2..5....5..0..2....1..2..3....0..3..4

Crossrefs

Cf. A214166.

Sequence in context: A145615 A215194 A201538 * A242446 A160013 A356687

Adjacent sequences: A214157 A214158 A214159 * A214161 A214162 A214163

Keyword

nonn

Author

R. H. Hardin, Jul 05 2012

Status

approved