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A027377
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Number of irreducible polynomials of degree n over GF(4); dimensions of free Lie algebras.
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14
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1, 4, 6, 20, 60, 204, 670, 2340, 8160, 29120, 104754, 381300, 1397740, 5162220, 19172790, 71582716, 268431360, 1010580540, 3817733920, 14467258260, 54975528948, 209430785460, 799644629550, 3059510616420
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Apart from initial terms, exponents in expansion of A065419 as a product zeta(n)^(-a(n)).
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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.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..200
G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for sequences related to Lyndon words
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FORMULA
| Sum mu(d)*4^(n/d)/n; d|n.
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MAPLE
| A027377 := proc(n) local d, s; if n = 0 then RETURN(1); else s := 0; for d in divisors(n) do s := s+mobius(d)*4^(n/d); od; RETURN(s/n); fi; end;
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MATHEMATICA
| a[n_] := Sum[MoebiusMu[d]*4^(n/d), {d, Divisors[n]}] / n; a[0] = 1; Table[a[n], {n, 0, 23}](* From Jean-François Alcover, Nov 29 2011 *)
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PROG
| (PARI) a(n)=if(n, sumdiv(n, d, moebius(d)<<(2*n/d))/n, 1) \\ Charles R Greathouse IV, Nov 29 2011
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CROSSREFS
| Cf. A001037, A027376, A054719.
Sequence in context: A026788 A079435 A088015 * A048789 A038069 A143391
Adjacent sequences: A027374 A027375 A027376 * A027378 A027379 A027380
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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