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A001693
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Number of degree-n irreducible polynomials over GF(7); dimensions of free Lie algebras.
(Formerly M4373 N1838)
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4
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1, 7, 21, 112, 588, 3360, 19544, 117648, 720300, 4483696, 28245840, 179756976, 1153430600, 7453000800, 48444446376, 316504099520, 2077057800300, 13684147881600, 90467419857752, 599941851861744
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OFFSET
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0,2
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REFERENCES
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E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84.
M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 79.
G. J. Simmons, The number of irreducible polynomials of degree n over GF(p), Amer. Math. Monthly, 77 (1970), 743-745.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
G. Viennot, Algebres de Lie Libres et Monoides Libres, Lecture Notes in Mathematics 691, Springer verlag 1978.
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LINKS
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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.
Index entries for sequences related to Lyndon words
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FORMULA
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a(n) = (1/n)*Sum_{d|n} mu(d)*7^(n/d).
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MAPLE
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with(numtheory); A001693 := proc(n) local d, s; if n = 0 then RETURN(1); else s := 0; for d in divisors(n) do s := s+mobius(d)*7^(n/d); od; RETURN(s/n); fi; end;
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MATHEMATICA
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a[n_]:=(1/n)*Sum[MoebiusMu[d]*7^(n/d), {d, Divisors[n]}]; a[0] = 1; Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Aug 31 2011, after formula *)
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CROSSREFS
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Cf. A027376, A000031, A001037.
Sequence in context: A219152 A038184 A001185 * A061961 A028248 A032032
Adjacent sequences: A001690 A001691 A001692 * A001694 A001695 A001696
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Description corrected by Vladeta Jovovic, Feb 09 2001.
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STATUS
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approved
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