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, 4, 15, 80, 362, 1832, 8994, 46384, 238838, 1257824

Offset

0,2

Comments

Some boundary mutually non-adjacent 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 non-singular edge, an end and an internal side of it. n is the number of internal edges plus half of the number of non-singular 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), 197-217.

Example

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

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