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A006390
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Number of unrooted loopless planar n-edge maps.
(Formerly M1468)
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0
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1, 1, 2, 5, 14, 49, 240, 1259, 7570, 47996, 319518, 2199295, 15571610, 112773478, 832809504, 6253763323, 47650870538, 376784975116, 2871331929096, 22647192990256, 180277915464664
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Walsh, T. R. S.; Generating nonisomorphic maps without storing them. SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.
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LINKS
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Table of n, a(n) for n=0..20.
V. A. Liskovets and T. R. S. Walsh, Counting Unrooted Loopless Planar Maps [Extended abstract]
V. A. Liskovets and T. R. S. Walsh, Counting unrooted loopless planar maps, Europ. J. Combin., 26:5 (2005), 651-663.
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FORMULA
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a(n)=(1/2n)[2(4n+1)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)=binomial(2n, (n-2)/2) if n is even and q(n)=2n*binomial(2n, (n-1)/2)/(n+1) if n is odd.
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CROSSREFS
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Cf. A000260.
Sequence in context: A079452 A081920 A224978 * A100597 A022562 A115340
Adjacent sequences: A006387 A006388 A006389 * A006391 A006392 A006393
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Valery A. Liskovets, Dec 01 2003
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STATUS
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approved
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