A074655 Number of Lyndon words (aperiodic necklaces) with 3n beads of 3 colors, n beads of each color.

1, 2, 14, 186, 2880, 50450, 952854, 19003474, 394394880, 8439756660, 185033201150, 4137181680698, 94020326259264, 2166105078791446, 50489825369325118, 1188777328563863850, 28236363841594782720, 675879582290807439794, 16289254212695836475436

Offset: 0

Author

Christian G. Bower, Aug 29 2002

Keywords

• nonn

Links

• Index entries for sequences related to Lyndon words

Crossrefs

Cf. A029808, A074651, A022553 (2n of 2 colors), A074656 (4n of 4 colors).

Formula

a(n) = 1/(3n) * Sum_{d|n} mu(n/d) * (3d)! / d!^3, a(0) = 1.

a(n) = A029808(n)*2 = A074651(n)/3.

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 24 2015