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Search: id:A090371
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| A090371 |
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Number of unrooted planar 2-constellations with n digons. Also number of n-edge unrooted planar Eulerian maps with bicolored faces. |
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3
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| 1, 3, 6, 20, 60, 291, 1310, 6975, 37746, 215602, 1262874, 7611156, 46814132, 293447817, 1868710728, 12068905911, 78913940784, 521709872895, 3483289035186, 23464708686960
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) is also the number of unrooted planar hypermaps with n darts up to orientation-preserving homeomorphism (darts are semi-edges in the particular case of ordinary maps). - Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 13 2006
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LINKS
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M. Bousquet-Melou and G. Schaeffer, Enumeration of planar constellations, Adv. in Appl. Math. v.24 (2000), 337-368.
A. Mednykh and R. Nedela, Counting unrooted hypermaps on closed orientable surface, 18th Intern. Conf. Formal Power Series & Algebr. Comb., Jun 19, 2006, San Diego, California (USA).
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EXAMPLE
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The 3 Eulerian maps with 2 edges are the digon and two figure eight graphs ("8") in which both loops are colored, resp., black or white.
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MAPLE
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with(numtheory): C_2 := proc(n) local s, d; if n=0 then RETURN(1) else s := -2^n*binomial(2*n, n); for d in divisors(n) do s := s+phi(n/d)*2^d*binomial(2*d, d) od; RETURN((3/(2*n))*(2^n*binomial(2*n, n)/((n+1)*(n+2))+s/2)); fi; end;
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CROSSREFS
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Cf. A000257, A069727, A090372, A118094.
Sequence in context: A052408 A005558 A138350 this_sequence A123559 A019017 A019049
Adjacent sequences: A090368 A090369 A090370 this_sequence A090372 A090373 A090374
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KEYWORD
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easy,nonn
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AUTHOR
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Valery Liskovets (liskov(AT)im.bas-net.by), Dec 01 2003
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