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

Author

Vincent Delecroix, Mar 29 2018

Keywords

• nonn

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, and A. Zorich, Enumeration of meanders and Masur-Veech volumes, arXiv:1705.05190 [math.GT], 2017.
• Index entries for sequences related to meanders

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.

Formula

Known asymptotics: Sum_{n <= N} a(n) ~ 70 N^7/(9 Pi^6).