0,2

Number of Lyndon words of length n on {1,2,3}. A Lyndon word is primitive (not a power of another word) and is earlier in lexicographic order than any of its cyclic shifts. - John W. Layman (layman(AT)math.vt.edu), Jan 24 2006

Exponents in an expansion of the Hardy-Littlewood constant product(1-(3*p-1)/(p-1)^3, p prime >= 5), whose decimal expansion is in A065418: the constant equals product_{n>=2} (zeta(n)*(1-2^-n)*(1-3^-n))^-a(n). - Michael Somos, Apr 05 2003

E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84.

E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.

M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 79.

G. Viennot, Algebres de Lie Libres et Monoides Libres, Lecture Notes in Mathematics 691, Springer verlag 1978.

T. D. Noe, Table of n, a(n) for n=0..200

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

G. Niklasch, Some number theoretical constants: 1000-digit values

Index entries for sequences related to Lyndon words

Sum mu(d)*3^(n/d)/n; d|n. (1-3x)=Product_{n>0} (1-x^n)^a(n).

A027376 := proc(n) local d, s; if n = 0 then RETURN(1); else s := 0; for d in divisors(n) do s := s+mobius(d)*3^(n/d); od; RETURN(s/n); fi; end;

a[0]=1; a[n_] := Module[{ds=Divisors[n], i}, Sum[MoebiusMu[ds[[i]]]3^(n/ds[[i]]), {i, 1, Length[ds]}]/n]

(PARI) a(n)=if(n<1, n==0, sumdiv(n, d, moebius(n/d)*3^d)/n)

Cf. A001693, A000031, A001037, A027375, A027377, A054718, A001867, A102660.

Sequence in context: A059197 A049974 A049972 this_sequence A038068 A101126 A119006

Adjacent sequences: A027373 A027374 A027375 this_sequence A027377 A027378 A027379

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).