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Search: id:A069727
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| A069727 |
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Number of nonisomorphic unrooted Eulerian planar maps with n edges (Eulerian means that all vertices are of even valency; there is an Eulerian cycle). |
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8
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| 1, 1, 2, 4, 12, 34, 154, 675, 3534, 18985, 108070, 632109, 3807254, 23411290, 146734695, 934382820, 6034524474, 39457153432, 260855420489, 1741645762265, 11732357675908
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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V. A. Liskovets and T. R. S. Walsh, Enumeration of Eulerian and unicursal planar maps, Discr. Math., 282 (2004), 209-221.
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FORMULA
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There is an easy formula.
a(n)=(1/(2n))[3*2^(n-1)binomial(2n, n)/((n+1)(n+2)) +sum_{0<k<n, k|n}phi(n/k)d(n/k)2^(k-2)binomial(2k, k)]+q(n) where phi is the Euler function A000010, q(n)=2^((n-4)/2)binomial{9n, n/2)/(n+2) if n is even, q(n)=2^((n-1)/2)binomial(n-1, (n-1)/2)/(n+1) if n is odd, d(n)=4, if n is even and d(n)=3 if n is odd. - Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 17 2005
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CROSSREFS
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Cf. A069724, A000257, A069720.
Sequence in context: A005028 A108530 A001895 this_sequence A019447 A112083 A089965
Adjacent sequences: A069724 A069725 A069726 this_sequence A069728 A069729 A069730
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002
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