A287967 Number of Dyck paths of semilength n such that no level has more than three peaks.

1, 1, 2, 5, 13, 40, 119, 376, 1202, 3916, 12920, 42974, 143989, 485623, 1646056, 5601850, 19127858, 65491001, 224750426, 772816118, 2661800949, 9180835248, 31703037147, 109586025511, 379124973003, 1312592051481, 4547284385059, 15761969520682, 54660238286990

Offset: 0

Author

Alois P. Heinz, Jun 03 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Manosij Ghosh Dastidar and Michael Wallner, Bijections and congruences involving lattice paths and integer compositions, arXiv:2402.17849 [math.CO], 2024. See p. 19.
• Wikipedia, Counting lattice paths

Crossrefs

Column k=3 of A287847.

Cf. A000108.

Formula

a(n) = A287847(n,3).

a(n) = A000108(n) for n <= 3.