A029808 Number of Lyndon words (aperiodic necklaces) with 3n beads of 3 colors, n beads of each color. One color labeled, the other two unlabeled.

1, 7, 93, 1440, 25225, 476427, 9501737, 197197440, 4219878330, 92516600575, 2068590840349, 47010163129632, 1083052539395723, 25244912684662559, 594388664281931925, 14118181920797391360, 337939791145403719897

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Index entries for sequences related to Lyndon words

Formula

1/(6n) * sum over d|n of {mu(n/d) * (3d)! / d!^3}.

Maple

A029808 := proc(n)
    add(numtheory[mobius](n/d)*(3*d)!/(d!)^3, d=numtheory[divisors](n)) ;
    %/6/n ;
end proc:
seq(A029808(n), n=1..10) ;

Prog

(PARI) for(n=1, 23, print(1/(6*n)*sumdiv(n, d, moebius(n/d)*(3*d)!/d!^3)))

Crossrefs

Inverse Witt transform of A006178.

Sequence in context: A278687 A292227 A006178 * A379910 A089915 A370939

Adjacent sequences: A029805 A029806 A029807 * A029809 A029810 A029811

Keyword

nonn

Author

Lionel Levine (levine(AT)ultranet.com)

Extensions

More terms from Jason Earls, Aug 31 2001

Edited by Christian G. Bower, Aug 28 2002

Status

approved