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Search: id:A113183
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| A113183 |
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Number of unrooted two-face maps in the plane (considered up to orientation-preserving homeomorphism) with the faces of equal degree n: planar maps with a distinguished outside face. |
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+0
1
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| 1, 1, 2, 3, 8, 18, 58, 155, 546, 1592, 5774, 17798, 65676, 210362, 785248, 2588155, 9743348, 32832290, 124416022, 426685544, 1625465732, 5654938190, 21636274202, 76171463926, 292498386900, 1040120036300, 4006388161846, 14369121494126
(list; graph; listen)
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OFFSET
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1,3
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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)=(1/n)Sum_{k|n}phi(k)binomial((n/k)-1, floor(n/(2k)))^2 where phi(k) is the Euler function A000010.
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EXAMPLE
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There exist 2 maps in the plane with two triangular faces:
a triangle and a map consisting of a 2-path and a loop in its
middle vertex that separates both ends. Therefore a(3)=2.
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CROSSREFS
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Cf. A113181, A060404.
Sequence in context: A005957 A158448 A073192 this_sequence A157015 A041205 A002356
Adjacent sequences: A113180 A113181 A113182 this_sequence A113184 A113185 A113186
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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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