A300901 Number of closed meanders with 2n crossings and 5 digons.

16, 40, 168, 280, 544, 1152, 1560, 2640, 3504, 5824, 6552, 12000, 11456, 19176, 18648, 31312, 30640, 50064, 43736, 71392, 62304, 104800, 87672, 141048, 121968, 191632, 154200, 255192, 209536, 327360, 265880, 435960, 328176, 533688, 419064, 649272, 525280

Offset

4,1

Comments

A meander together with the horizontal line separates the plane into several connected components. Each component has a given number of edges which is always an even number. The digons (or bigons) are the faces with least number of edges, that is 2. Equivalently, the number of digons is the number of arches between adjacent sites ("minimal arches") where the two extremal ones are considered adjacent.

Links

Vincent Delecroix, Table of n, a(n) for n = 4..164

V. Delecroix, E. Goujard, P. Zograf, A. Zorich Enumeration of meanders and Masur-Veech volumes, arXiv:1705.05190 [math.GT], 2017.

Index entries for sequences related to meanders

Formula

Known asymptotics: Sum_{n <= N} a(n) ~ 16 N^5/(3 Pi^4).

Crossrefs

A002618 is the number of closed meanders with 4 digons. A301940 is the number of meanders with 6 digons. A005315 is the total number of closed meanders.

Sequence in context: A205248 A205186 A197903 * A174086 A174081 A230802

Adjacent sequences: A300898 A300899 A300900 * A300902 A300903 A300904

Keyword

nonn

Author

Vincent Delecroix, Mar 14 2018

Status

approved