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Search: id:A001693
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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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+0
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
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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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CROSSREFS
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Cf. A027376, A000031, A001037.
Sequence in context: A121157 A038184 A001185 this_sequence A061961 A028248 A032032
Adjacent sequences: A001690 A001691 A001692 this_sequence 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 (njas(AT)research.att.com).
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EXTENSIONS
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Description corrected by Vladeta Jovovic (vladeta(AT)EUnet.yu), Feb 09, 2001.
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