

A090376


Number of rooted generalized quadrangular dissections of weight n of a closed disk: planar maps having the external face bounded by a polygon and all internal faces of size 4.


1




OFFSET

0,2


COMMENTS

Some boundary mutually nonadjacent nodes of valency 2 are marked as singular; (boundary) edges incident to them are also called singular. The maps are considered up to rotations and reflections. Rooting means distinguishing a nonsingular edge, an end and an internal side of it. n is the number of internal edges plus half of the number of nonsingular boundary edges.
No formula is known. For any generalized quadrangular dissection, s==n (mod 2), where s is the number of singular nodes.


LINKS

Table of n, a(n) for n=0..9.
V. A. Liskovets, A reductive technique for enumerating nonisomorphic planar maps, Discr. Math., v.156 (1996), 197217.


EXAMPLE

The four rooted generalized quadrangular dissections of weight 1 are
...................____......____..
.X<X..X<X.../....\..../....\.
.............X<X..O..X<X..O
..............\____/....\____/.
.XO..XO....................
where O is the singular node and > is the rooted edgeend.


CROSSREFS

Cf. A006385.
Sequence in context: A243327 A179511 A111726 * A232042 A125307 A073479
Adjacent sequences: A090373 A090374 A090375 * A090377 A090378 A090379


KEYWORD

nonn,more


AUTHOR

Valery A. Liskovets, Dec 03 2003


STATUS

approved



