A214143 Number of 0..4 colorings of a 2 X (n+1) array circular in the n+1 direction with new values 0..4 introduced in row major order.

4, 17, 257, 3074, 40434, 522515, 6800539, 88363628, 1148860844, 14934544493, 194151313701, 2523957115862, 32811479230534, 426549073848551, 5545138556625743, 72086798766250976, 937128393589298304

Offset

1,1

Comments

Row 2 of A214141.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) + 50*a(n-2) - 116*a(n-3) - 361*a(n-4) + 106*a(n-5) + 312*a(n-6).

Empirical: 3^n/4 +13^(n+1)/120 -(-1)^n/6 +(-2)^(n+1)/5 -2*(-4)^n/15 +41/120. - R. J. Mathar, Jul 07 2012

Empirical g.f.: x*(4 - 23*x - 113*x^2 + 118*x^3 + 260*x^4) / ((1 - x)*(1 + x)*(1 + 2*x)*(1 - 3*x)*(1 + 4*x)*(1 - 13*x)). - Colin Barker, Jul 22 2018

Example

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

Crossrefs

Cf. A214141.

Sequence in context: A032073 A032083 A126776 * A320986 A302145 A015489

Adjacent sequences: A214140 A214141 A214142 * A214144 A214145 A214146

Keyword

nonn

Author

R. H. Hardin, Jul 05 2012

Status

approved