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Number of Lyndon words (aperiodic necklaces) with 3n beads of 3 colors, n beads of each color. One color labeled, the other two unlabeled.
4

%I #12 Oct 21 2021 10:32:02

%S 1,7,93,1440,25225,476427,9501737,197197440,4219878330,92516600575,

%T 2068590840349,47010163129632,1083052539395723,25244912684662559,

%U 594388664281931925,14118181920797391360,337939791145403719897

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

%H <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>

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

%p A029808 := proc(n)

%p add(numtheory[mobius](n/d)*(3*d)!/(d!)^3,d=numtheory[divisors](n)) ;

%p %/6/n ;

%p end proc:

%p seq(A029808(n),n=1..10) ;

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

%Y Inverse Witt transform of A006178.

%K nonn

%O 1,2

%A Lionel Levine (levine(AT)ultranet.com)

%E More terms from _Jason Earls_, Aug 31 2001

%E Edited by _Christian G. Bower_, Aug 28 2002