A391919 Triangle read by rows: T(n, k) is the number of singular meanders with n intersections having k tangential intersections.

1, 1, 1, 1, 4, 1, 2, 7, 14, 1, 3, 24, 36, 48, 1, 8, 47, 188, 166, 166, 1, 14, 168, 459, 1224, 730, 584, 1, 42, 352, 2112, 3601, 7202, 3138, 2092, 1, 81, 1296, 5166, 20664, 24880, 39808, 13328, 7616, 1, 262, 2851, 22808, 57888, 173664, 158244, 210992, 56204, 28102, 1

Offset

0,5

Comments

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

Links

Yury Belousov, Rows n = 0..19 of triangle, flattened.

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.

Example

Triangle begins:
  1;
  1,  1;
  1,  4,  1;
  2,  7, 14,  1;
  3, 24, 36, 48, 1;
  ...

Crossrefs

Column 0 is A005316.

Main diagonal gives A000012.

Subdiagonal gives A082590.

Row sums give A393122.

Sequence in context: A084460 A216863 A394216 * A120578 A096249 A081454

Adjacent sequences: A391916 A391917 A391918 * A391920 A391921 A391922

Keyword

nonn,tabl,hard

Author

Yury Belousov, Jan 27 2026

Status

approved