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A338417 a(n) is the number of length-n palindromic ballot sequences. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A109522 A052959 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

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Last modified May 7 06:18 EDT 2021. Contains 343636 sequences. (Running on oeis4.)