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A338418 a(n) is the number of length-n ballot sequences whose reversals are also ballot sequences. 2
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 (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..24.

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,more

AUTHOR

Rémy Sigrist, Oct 25 2020

STATUS

approved

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Last modified May 18 15:25 EDT 2021. Contains 343995 sequences. (Running on oeis4.)