|
| |
|
|
A027376
|
|
Number of ternary irreducible polynomials of degree n; dimensions of free Lie algebras.
|
|
23
| |
|
|
1, 3, 3, 8, 18, 48, 116, 312, 810, 2184, 5880, 16104, 44220, 122640, 341484, 956576, 2690010, 7596480, 21522228, 61171656, 174336264, 498111952, 1426403748, 4093181688, 11767874940, 33891544368, 97764009000, 282429535752
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| 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
|
|
|
REFERENCES
| 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.
|
|
|
LINKS
| 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 [Cached copy]
Index entries for sequences related to Lyndon words
|
|
|
FORMULA
| Sum mu(d)*3^(n/d)/n; d|n. (1-3x)=Product_{n>0} (1-x^n)^a(n).
|
|
|
MAPLE
| 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;
|
|
|
MATHEMATICA
| a[0]=1; a[n_] := Module[{ds=Divisors[n], i}, Sum[MoebiusMu[ds[[i]]]3^(n/ds[[i]]), {i, 1, Length[ds]}]/n]
|
|
|
PROG
| (PARI) a(n)=if(n<1, n==0, sumdiv(n, d, moebius(n/d)*3^d)/n)
|
|
|
CROSSREFS
| Cf. A001693, A000031, A001037, A027375, A027377, A054718, A001867, A102660.
Sequence in context: A059197 A049974 A049972 * A190659 A202536 A038068
Adjacent sequences: A027373 A027374 A027375 * A027377 A027378 A027379
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
