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Search: id:A103942
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| A103942 |
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Number of unrooted n-edge isthmusless maps in the plane (planar with a distinguished outside face). |
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+0
2
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| 1, 3, 9, 38, 187, 1120, 7083, 47990, 337676, 2455517, 18310155, 139447034, 1080773098, 8502896424, 67763884363, 546147639926, 4445389286380, 36501274080076, 302060508150976, 2517213486505592
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
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LINKS
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V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.
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FORMULA
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a(n)=(1/(2n))[(5n^2+13n+2)binomial(4n, n)/((n+1)(3n+1)(3n+2)) + sum_{0<k<n, k|n}phi(n/k)binomial(4k, k)+q(n)] where phi is the Euler function (A000010), q(n)=0 if n is even and q(n)=(n-1)binomial(2n, (n-1)/2)/(n+1) if n is odd.
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CROSSREFS
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Cf. A027836, A103941, A000260.
Sequence in context: A149024 A149025 A133222 this_sequence A030928 A030912 A030892
Adjacent sequences: A103939 A103940 A103941 this_sequence A103943 A103944 A103945
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KEYWORD
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easy,nonn
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AUTHOR
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Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 17 2005
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