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A288114 Number of Dyck paths of semilength n such that each level has exactly seven peaks or no peaks. 2
1, 0, 0, 0, 0, 0, 0, 1, 1, 7, 22, 48, 93, 180, 331, 575, 1150, 3578, 13268, 50808, 217173, 881980, 3064454, 9169075, 24605669, 61450068, 147038896, 347902716, 860591396, 2411664484, 8038395295, 30845855094, 126173520602, 513951305502, 1996531969713 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

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, 7$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, 7, 7]];

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

CROSSREFS

Column k=7 of A288108.

Sequence in context: A244243 A223833 A014073 * A129109 A224141 A002412

Adjacent sequences:  A288111 A288112 A288113 * A288115 A288116 A288117

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 05 2017

STATUS

approved

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Last modified November 25 14:47 EST 2020. Contains 338625 sequences. (Running on oeis4.)