A074652 -id:A074652 - cp's OEIS frontend

A074656 Number of Lyndon words (aperiodic necklaces) with 4n beads of 4 colors, n beads of each color.

1, 6, 312, 30798, 3941280, 586637250, 96197630040, 16875655269942, 3111284137104000, 595909785174026400, 117634021776545937000, 23797087019979071174574, 4912693780461256332795168, 1031629572413246016139181538, 219809927417367517614451764984

Offset: 0

Christian G. Bower, Aug 29 2002

nonn

			For n=1 the 6 words are 0123 0132 0213 0231 0312 0321 . - _R. J. Mathar_, Oct 21 2021

Index entries for sequences related to Lyndon words

a(n)=A029809(n)*6. a(n) = A074652(n)/4.

1/(4n) * sum over d|n of {mu(n/d) * (4d)! / d!^4}.

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

A006175 Witt vector *4!.

Original entry on oeis.org

24, 972, 118592, 15210414, 2344956480, 377420590432, 67501965869568, 12329221295657241, 2383082885396731968, 467786496795764717088, 95188347941581635319296, 19578329367376510676884584

Offset: 1

Simon Plouffe

nonn

If c is the Witt transform of b then b(n) = Sum_{d|n} A074650(n/d, c(d)).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-108.
H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-107. (Annotated scanned copy)

Witt transform of A074652.

More terms and formula from Christian G. Bower, Aug 28 2002

cp's OEIS Frontend

A074656 Number of Lyndon words (aperiodic necklaces) with 4n beads of 4 colors, n beads of each color.

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