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

Author

Jacob A. Siehler, May 10 2006

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A003239.

Column k=3 of A208183.

Programs

Mathematica

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

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