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A288116 Number of Dyck paths of semilength n such that each level has exactly nine peaks or no peaks. 2
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 9, 37, 101, 227, 487, 1019, 2015, 3724, 6528, 11438, 24758, 81106, 330810, 1542486, 7723906, 35765450, 142808117, 494994177, 1533142713, 4370885515, 11737660709, 30111369545, 74286138919, 177289070957, 416431652499 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Counting lattice paths

MAPLE

b:= proc(n, k, j) option remember; `if`(n=j, 1, add(

      b(n-j, k, i)*(binomial(j-1, i-1)+binomial(i, k)

       *binomial(j-1, i-1-k)), i=1..min(j+k, n-j)))

    end:

a:= n-> `if`(n=0, 1, b(n, 9$2)):

seq(a(n), n=0..40);

MATHEMATICA

b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[b[n - j, k, i]*(Binomial[j - 1, i - 1] + Binomial[i, k]*Binomial[j - 1, i - 1 - k]), {i, 1, Min[j + k, n - j]}]];

a[n_] := If[n == 0, 1, b[n, 9, 9]];

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Jun 02 2018, from Maple *)

CROSSREFS

Column k=9 of A288108.

Sequence in context: A299290 A304290 A244245 * A165394 A213570 A271908

Adjacent sequences:  A288113 A288114 A288115 * A288117 A288118 A288119

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 05 2017

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)