cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A090376 #9 Jan 14 2020 03:24:29
%S A090376 1,4,15,80,362,1832,8994,46384,238838,1257824
%N 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.
%C A090376 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.
%C A090376 No formula is known. For any generalized quadrangular dissection, s==n (mod 2), where s is the number of singular nodes.
%H A090376 V. A. Liskovets, <a href="http://dx.doi.org/10.1016/0012-365X(94)00347-L">A reductive technique for enumerating nonisomorphic planar maps</a>, Discr. Math., v.156 (1996), 197-217.
%e A090376 The four rooted generalized quadrangular dissections of weight 1 are
%e A090376 ...................____......____..
%e A090376 .X<---X..X---<X.../....\..../....\.
%e A090376 .|....|..|....|..X<--X..O..X--<X..O
%e A090376 .|....|..|....|...\____/....\____/.
%e A090376 .X----O..X----O....................
%e A090376 where O is the singular node and -> is the rooted edge-end.
%Y A090376 Cf. A006385.
%K A090376 nonn,more
%O A090376 0,2
%A A090376 _Valery A. Liskovets_, Dec 03 2003