A338417 a(n) is the number of length-n palindromic ballot sequences.

1, 1, 1, 2, 1, 3, 3, 7, 4, 14, 9, 33, 29, 96, 64, 254, 163, 692, 466, 2140, 1697, 7284, 5161, 24421, 16456, 81892, 55698, 284924, 188134, 1047372, 785292, 4159714, 3015604, 16667771, 11495031, 66976871, 46966691, 275446751, 184362732, 1137178180, 767632663, 4898013187, 3510305457, 22233966251, 16073243746

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

Table of n, a(n) for n=0..44.

Rémy Sigrist, PARI program for A338417

Formula

a(n) <= A338418(n).

Example

For n = 5:
- the following length-5 ballot sequences are palindromic:
     (1, 1, 1, 1, 1)
     (1, 1, 2, 1, 1)
     (1, 2, 1, 2, 1)
- so a(5) = 3.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000085, A338418.

Sequence in context: A052959 A346473 A257702 * A034399 A005292 A183256

Adjacent sequences: A338414 A338415 A338416 * A338418 A338419 A338420

Keyword

nonn

Author

Rémy Sigrist, Oct 25 2020

Extensions

a(35)-a(44) from Bert Dobbelaere, Oct 31 2020

Status

approved