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Search: id:A103937
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| A103937 |
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Number of unrooted n-edge maps in the plane (planar with a distinguished outside face). |
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+0
1
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| 2, 6, 26, 150, 1032, 8074, 67086, 586752, 5317226, 49592424, 473357994, 4606116310, 45554761836, 456848968518, 4637014782748, 47563495004742, 492422043299964, 5140194991046122, 54053208147441474, 572191817441284272
(list; graph; listen)
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OFFSET
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1,1
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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))[3^n*binomial(2n, n)/(n+1) +sum_{0<k<n, k|n}phi(n/k)3^k*binomial(2k, k)]+q(n) where phi is the Euler function A000010, q(n)=0 if n is even and q(n)=3^((n-1)/2)binomial(n-1, (n-1)/2)/(n+1) if n is odd.
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CROSSREFS
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Cf. A005159, A005470.
Sequence in context: A125224 A052844 A052859 this_sequence A159311 A000629 A032187
Adjacent sequences: A103934 A103935 A103936 this_sequence A103938 A103939 A103940
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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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