|
| |
|
|
A090371
|
|
Number of unrooted planar 2-constellations with n digons. Also number of n-edge unrooted planar Eulerian maps with bicolored faces.
|
|
10
|
|
|
|
1, 3, 6, 20, 60, 291, 1310, 6975, 37746, 215602, 1262874, 7611156, 46814132, 293447817, 1868710728, 12068905911, 78913940784, 521709872895, 3483289035186, 23464708686960
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
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, Apr 13 2006
|
|
|
REFERENCES
|
A. Mednykh and R. Nedela, Enumeration of unrooted hypermaps of a given genus, Discr. Math., 310 (2010), 518-526. [From N. J. A. Sloane, Dec 19 2009]
|
|
|
LINKS
|
R. J. Mathar, Table of n, a(n) for n = 1..100
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).
Timothy R. Walsh, Generating nonisomorphic maps and hypermaps without storing them, to appear in Proceedings of GASCom2012
|
|
|
EXAMPLE
|
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.
|
|
|
MAPLE
|
A090371 := proc(n)
local s, d;
if n=0 then
1 ;
else
s := -2^n*binomial(2*n, n);
for d in numtheory[divisors](n) do
s := s+ numtheory[phi](n/d)*2^d*binomial(2*d, d)
od;
3/(2*n)*(2^n*binomial(2*n, n)/((n+1)*(n+2))+s/2);
fi;
end proc:
|
|
|
CROSSREFS
|
Cf. A000257, A069727, A090372, A118094.
Sequence in context: A148603 A185172 A173110 * A168594 A123559 A162171
Adjacent sequences: A090368 A090369 A090370 * A090372 A090373 A090374
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Valery A. Liskovets, Dec 01 2003
|
|
|
STATUS
|
approved
|
| |
|
|
