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Search: id:A035109
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| A035109 |
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Numerators in expansion of a certain Dirichlet series. |
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+0
1
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OFFSET
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0,3
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COMMENT
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a(n) is also the number of orbits of length n for the map SxT where S has one orbit of each length and T has one orbit of each odd length. [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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REFERENCES
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Apisit Pakapongpun and Thomas Ward, Functorial orbit counting, Journal of Integer Sequences, 12 (2009) Article 09.2.4. [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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LINKS
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M. Baake and R. V. Moody, Similarity submodules and semigroups in Quasicrystals and Discrete Geometry, ed. J. Patera, Fields Institute Monographs, vol. 10 AMS, Providence, RI (1998) pp. 1-13.
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FORMULA
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zeta(s)*Product((1+p^-s)/(1-p^(1-s))), p>2.
a(n)=(1/n)sumdiv(n,d,mu(n/d)sum(d,e,e)sum(d,e odd only,e) [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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EXAMPLE
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a(6)=(1/6)(mu(6)*1*1+mu(3)*3*1+mu(2)*4*4+mu(1)*4*12)=5 [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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PROGRAM
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(PARI) a(n)=(1/n)*sumdiv(n, d, moebius(n/d)*sigma(d)*sumdiv(d, e, if(e%2, e, 0))) [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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CROSSREFS
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Sequence in context: A158552 A021663 A099218 this_sequence A101263 A088515 A100122
Adjacent sequences: A035106 A035107 A035108 this_sequence A035110 A035111 A035112
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KEYWORD
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nonn,easy,more
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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