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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 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.)