A118644 Number of distinct (n red, n blue, n green)-bead necklaces.

1, 2, 16, 188, 2896, 50452, 953056, 19003476, 394397776, 8439756848, 185033251616, 4137181680700, 94020327215200, 2166105078791448, 50489825388328608, 1188777328563914488, 28236363841989180496, 675879582290807439796, 16289254212704277185152

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..700

Formula

Sum_{d|n} ( phi(n/d)(3d Choose d)(2d Choose d) )/3n for n>0. [Corrected by several correspondents, Mar 04 2010]

a(n) ~ 3^(3*n-1/2) / (2*Pi*n^2). - Vaclav Kotesovec, Aug 23 2015

Mathematica

f[n_] := Plus @@ (EulerPhi[n/# ]Binomial[3#, # ]Binomial[2#, # ] & /@ Divisors[n])/(3n)

Crossrefs

Cf. A003239.

Column k=3 of A208183.

Sequence in context: A011553 A291816 A123898 * A183205 A006335 A273591

Adjacent sequences: A118641 A118642 A118643 * A118645 A118646 A118647

Keyword

easy,nonn

Author

Jacob A. Siehler, May 10 2006

Status

approved