A393122 Number of singular meanders with n intersections.

1, 2, 6, 24, 112, 576, 3180, 18540, 112840, 711016, 4610036, 30614932, 207498060, 1431260984, 10024424284, 71158769844, 511160782120, 3710968813976, 27198487483336, 201060296071624, 1497907249045496, 11238798692083888

Offset

0,2

Comments

Singular meanders are a generalization of standard (open) meanders (A005316) allowing tangential intersections.

Links

Table of n, a(n) for n=0..21.

Yury Belousov, Singular meanders, Zap. Nauchn. Sem. POMI, 549 (2025), 49-64.

Yury Belousov, Prime Factorization of Meanders, arXiv:2112.10289 [math.CO], 2025.

Yury Belousov, C++ code for generating the sequence, GitHub.

Formula

a(n) = Sum_{k=0..n} A391919(n, k).

Example

For n = 1, a(1) = 2. There are 2 singular meanders with a single intersection: one with a transverse intersection and one with a tangential intersection.

Crossrefs

Row sums of triangle A391919.

Sequence in context: A168490 A118376 A212884 * A375923 A085486 A152318

Adjacent sequences: A393119 A393120 A393121 * A393123 A393124 A393125

Keyword

nonn,hard,more

Author

Yury Belousov, Feb 02 2026

Status

approved