A301940 Number of closed meanders with 2n crossings and 6 digons.

2, 16, 110, 416, 1470, 4128, 9102, 20240, 40106, 71312, 127426, 203056, 336070, 491392, 790126, 1067160, 1650530, 2086720, 3180030, 3878952, 5768170, 6771680, 9871350, 11231064, 16241094, 17936352, 25665290, 27729640, 39210350, 41583104, 58341778, 60751880, 84510650

Offset

3,1

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

Table of n, a(n) for n=3..35.

V. Delecroix, E. Goujard, P. Zograf, and 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) ~ 70 N^7/(9 Pi^6).

Crossrefs

A002618 is the number of closed meanders with 4 digons. A300901 is the number of closed meanders with 5 digons. A005315 is the total number of closed meanders.

Sequence in context: A329550 A208137 A207435 * A359758 A370245 A370270

Adjacent sequences: A301937 A301938 A301939 * A301941 A301942 A301943

Keyword

nonn

Author

Vincent Delecroix, Mar 29 2018

Status

approved