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

0,3

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

Formula

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

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

Crossrefs

Column k=3 of A287847.

Cf. A000108.

Sequence in context: A127986 A255600 A320809 * A133448 A149862 A149863

Adjacent sequences: A287964 A287965 A287966 * A287968 A287969 A287970

Keyword

nonn

Author

Alois P. Heinz, Jun 03 2017

Status

approved