A214181 Number of 0..6 colorings of an n X 3 array circular in the 3 direction with new values 0..6 introduced in row major order.

1, 18, 1046, 108893, 13701111, 1808609113, 241491378451, 32332391658753, 4331663509964171, 580414863999963833, 77774694477831007731, 10421780348518296089713, 1396517647955429913843931

Offset

1,2

Comments

Column 2 of A214187.

Links

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

Formula

Empirical: a(n) = 179*a(n-1) - 6468*a(n-2) + 59396*a(n-3) - 94336*a(n-4).

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

G.f.: x*(1 - 161*x + 4292*x^2 - 21313*x^3) / ((1 - 2*x)*(1 - 11*x)*(1 - 32*x)*(1 - 134*x)).

a(n) = (2^(n-4)*(67^(n-1)+9) + 11^(n-1) + 3*2^(5*n-7))/3.

(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..0..3....3..0..1....1..2..3....1..2..3....1..2..3....1..0..3
..3..4..1....0..3..1....0..1..2....3..0..1....0..1..4....0..1..4....3..4..0
..4..0..2....1..4..0....1..0..3....4..1..5....4..2..0....1..0..5....0..5..1

Crossrefs

Cf. A214187.

Sequence in context: A363103 A073960 A095786 * A275653 A214232 A146197

Adjacent sequences: A214178 A214179 A214180 * A214182 A214183 A214184

Keyword

nonn

Author

R. H. Hardin, Jul 07 2012

Status

approved