A214167 Number of 0..5 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..5 introduced in row major order.

1, 1, 4, 11, 41, 161, 694, 3151, 14851, 71621, 350384, 1729091, 8577661, 42686281, 212828074, 1062335831, 5306276471, 26515196141, 132527465764, 662491871371, 3312023159281, 16558807553201, 82790113735454, 413938797983711

Offset

1,3

Comments

Row 1 of A214166.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) -30*a(n-2) +20*a(n-3) +31*a(n-4) -30*a(n-5).

Empirical: a(n) = 2^n/9 +3/16 -53*(-1)^n/144 +3^n/16 +5^n/144. - R. J. Mathar, Jul 09 2012

Empirical: G.f.: x*(1 - 9*x + 24*x^2 - 19*x^3) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 5*x)). - Colin Barker, Apr 22 2019

Example

Some solutions for n=8
..0..1..0..2..0..1..0..1..2........0..1..0..1..0..1..0..2..3

Crossrefs

Cf. A214166.

Sequence in context: A149270 A306188 A307702 * A278988 A214188 A214239

Adjacent sequences: A214164 A214165 A214166 * A214168 A214169 A214170

Keyword

nonn

Author

R. H. Hardin, Jul 05 2012

Status

approved