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A300901
Number of closed meanders with 2n crossings and 5 digons.
2
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
V. Delecroix, E. Goujard, P. Zograf, A. Zorich Enumeration of meanders and Masur-Veech volumes, arXiv:1705.05190 [math.GT], 2017.
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
KEYWORD
nonn
AUTHOR
Vincent Delecroix, Mar 14 2018
STATUS
approved