A288320 Number of Dyck paths of semilength n such that each positive level has exactly four peaks.

1, 0, 0, 0, 1, 0, 0, 0, 0, 5, 45, 105, 70, 0, 25, 525, 4950, 26950, 94605, 226925, 383525, 507000, 1016475, 5047875, 26940475, 117108550, 414703200, 1223146475, 3089625550, 7073320775, 16715232600, 48599763900, 175648700900, 673443954000, 2444611549450

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(i, k)
      *binomial(j-1, i-1-k)), i=1..min(j+k, n-j)))
    end:
a:= n-> `if`(n=0, 1, b(n, 4$2)):
seq(a(n), n=0..35);

Mathematica

b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[b[n - j, k, i]*(Binomial[i, k]*Binomial[j - 1, i - 1 - k]), {i, 1, Min[j + k, n - j]}]];
a[n_] := If[n == 0, 1, b[n, 4, 4]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jun 02 2018, from Maple *)

Crossrefs

Column k=4 of A288318.

Cf. A000108.

Sequence in context: A341383 A214711 A216767 * A003185 A302276 A302726

Adjacent sequences: A288317 A288318 A288319 * A288321 A288322 A288323

Keyword

nonn

Author

Alois P. Heinz, Jun 07 2017

Status

approved