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

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for sequences related to Lyndon words

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.

Crossrefs

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

Sequence in context: A370940 A237852 A219874 * A381478 A268005 A158102

Adjacent sequences: A074652 A074653 A074654 * A074656 A074657 A074658

Keyword

nonn

Author

Christian G. Bower, Aug 29 2002

Extensions

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

Status

approved