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Search: id:A113788
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| A113788 |
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Number of irreducible multiple zeta values at weight n. |
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+0
3
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| 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 7, 8, 11, 13, 17, 21, 28, 34, 45, 56, 73, 92, 120, 151, 197, 250, 324, 414, 537, 687, 892, 1145, 1484, 1911, 2479, 3196, 4148, 5359, 6954, 9000, 11687, 15140, 19672, 25516, 33166, 43065, 56010, 72784, 94716, 123185
(list; graph; listen)
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OFFSET
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1,11
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COMMENT
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Basically a Mobius Transform of the Perrin sequence
Number of unlabeled (i.e. defined up to a rotation) maximal independent sets of the n-cycle graph having n isomorphic representatives. - Jean-Luc Marichal (jean-luc.marichal(AT)uni.lu), Jan 24 2007
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REFERENCES
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D. J. Broadhurst and D. Kreimner, Associated multiple zeta values with positive knots via Feynman diagrams up to 9 knots, Phys. Lett B Vol. 393 (1997) pp. 403-412
R. Bisdorff and J.-L. Marichal, Counting non-isomorphic maximal independent sets of the n-cycle graph, preprint, 2007.
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LINKS
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D. J. Broadhurst and D. Kreimer, Association ofmultiple zeta values with positive knots via Feynman diagrams up to 9 loopsUTAS-PHYS-96-44
R. Bisdorff and J.-L. Marichal, Counting non-isomorphic maximal independent sets of the n-cycle graph, preprint, 2007.
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FORMULA
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(1/n) * sum(d divides n) mu(n/d) Perrin(d) where Perrin(d)=A001608 starting 0, 2, 3, ...
A113788(n) = Sum(d divides n) mu(n/d) A127687(d) = (1/n)*(Sum(d divides n) mu(n/d) A001608(d)) - Jean-Luc Marichal (jean-luc.marichal(AT)uni.lu), Jan 24 2007
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MAPLE
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A001608 := proc(n::integer) if n = 0 then RETURN(3); elif n = 1 then RETURN(0); elif n = 2 then RETURN(2); else RETURN(A001608(n-2)+A001608(n-3)); fi; end: A113788 := proc(n::integer) local resul, d; resul :=0; for d from 1 to n do if n mod d = 0 then resul := resul +numtheory[mobius](n/d)*A001608(d); fi; od: RETURN(resul/n); end: for n from 1 to 60 do print(A113788(n)); od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 25 2006
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CROSSREFS
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Cf. A001608.
Cf. A127687.
Sequence in context: A035575 A036816 A018243 this_sequence A127207 A089047 A036811
Adjacent sequences: A113785 A113786 A113787 this_sequence A113789 A113790 A113791
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KEYWORD
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nonn
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 27 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 25 2006
More terms from Jean-Luc Marichal (jean-luc.marichal(AT)uni.lu), Jan 24 2007
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