A338418 a(n) is the number of length-n ballot sequences whose reversals are also ballot sequences.

1, 1, 1, 2, 3, 5, 11, 23, 50, 118, 283, 731, 1921, 5370, 14884, 43118, 130509, 397490, 1266010, 4077494, 13435445, 45687806, 157483627, 551205779, 1979511990, 7235039300, 26840154388, 101944730262, 392596623714, 1530559274958, 6072449285528, 24470393750806, 100062786402800

Offset

0,4

Comments

Ballot sequences B have positive terms, and for any finite prefix P of B and any k > 0, the number of occurrences of k in P is greater than or equal to the number of occurrences of k+1 in P.

Links

Bert Dobbelaere, Table of n, a(n) for n = 0..70

Rémy Sigrist, C++ program for A338418

Formula

a(n) >= A338417(n).

Example

For n = 5:
- the reversals of the following length-5 ballot sequences are also ballot sequences:
     (1, 1, 1, 1, 1)
     (1, 1, 1, 2, 1)
     (1, 1, 2, 1, 1)
     (1, 2, 1, 1, 1)
     (1, 2, 1, 2, 1)
- so a(5) = 5.

Prog

(C++) // See Links section.

Crossrefs

Cf. A000085, A167510, A338417.

Sequence in context: A173927 A027763 A233694 * A261810 A176499 A175234

Adjacent sequences: A338415 A338416 A338417 * A338419 A338420 A338421

Keyword

nonn

Author

Rémy Sigrist, Oct 25 2020

Extensions

More terms from Bert Dobbelaere, Apr 12 2026

Status

approved