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Search: id:A103941
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| A103941 |
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Number of unrooted loopless n-edge maps in the plane (planar with a distinguished outside face). |
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+0
2
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| 1, 2, 6, 22, 103, 614, 3872, 26414, 186988, 1367976, 10254326, 78461338, 610598818, 4821248244, 38546510368, 311560875422, 2542507084588, 20925300483992, 173530381632724, 1448900079476152
(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))[binomial(4n, n)/(3n+1) + 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)=binomial(2n, (n-1)/2) if n is odd.
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CROSSREFS
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Cf. A002293, A103942, A000260, A005470.
Sequence in context: A000140 A079263 A129815 this_sequence A064643 A129535 A014371
Adjacent sequences: A103938 A103939 A103940 this_sequence A103942 A103943 A103944
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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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