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A090376
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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. 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.
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1
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OFFSET
| 0,2
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COMMENTS
| No formula is known. For any generalized quadrangular dissection, s==n (mod 2), where s is the number of singular nodes.
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REFERENCES
| V. A. Liskovets, A reductive technique for enumerating nonisomorphic planar maps, Discr. Math., 156 (1996), 197-217.
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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.
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CROSSREFS
| Cf. A006385.
Sequence in context: A002467 A179511 A111726 * A125307 A073479 A147690
Adjacent sequences: A090373 A090374 A090375 * A090377 A090378 A090379
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KEYWORD
| more,nonn
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AUTHOR
| Valery Liskovets (liskov(AT)im.bas-net.by), Dec 03 2003
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