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Search: id:A113181
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| A113181 |
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Number of unrooted two-vertex (or, dually, two-face) regular planar maps of even valency 2n considered up to orientation-preserving homeomorphism. |
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4
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| 1, 3, 14, 95, 859, 9130, 106039, 1297295, 16428300, 213388961, 2827645453, 38086408002, 520062618300, 7184570776213, 100256059855188, 1411319038583375, 20021022607979629, 285965560309310708
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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M. Bousquet, G. Labelle and P. Leroux, Enumeration of planar two-face maps, Discrete Math., vol. 222 (2000), 1-25.
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FORMULA
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a(n)=binomial(2n, n)/4+(1/(4n))Sum_{k|2n}phi(k)binomial((2n/k)-1), floor(n/k))^2 where phi(k) is the Euler function A000010.
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EXAMPLE
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There exist 3 planar maps with two 4-valent vertices:
a map with four parallel edges and two different maps with two
parallel edges and one loop in each vertex. Therefore a(2)=3.
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CROSSREFS
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Cf. A113182, A112944.
Sequence in context: A094369 A005772 A053984 this_sequence A136461 A007470 A074515
Adjacent sequences: A113178 A113179 A113180 this_sequence A113182 A113183 A113184
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KEYWORD
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nonn
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AUTHOR
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Valery A. Liskovets (liskov(AT)im.bas-net.by), Oct 19 2005
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