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

Author

Lionel Levine (levine(AT)ultranet.com)

Keywords

• nonn

Links

• Index entries for sequences related to Lyndon words

Crossrefs

Inverse Witt transform of A006178.

Programs

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) ;

PARI

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

Formula

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

Extensions

More terms from Jason Earls, Aug 31 2001

Edited by Christian G. Bower, Aug 28 2002