A372033 The total number of levels visited by all Motzkin paths of length n.

1, 1, 3, 7, 18, 46, 121, 323, 875, 2395, 6611, 18371, 51337, 144145, 406420, 1150126, 3265412, 9298372, 26547710, 75978322, 217921336, 626287520, 1803176384, 5200298000, 15020569818, 43447201226, 125837214564, 364911724264, 1059404265599, 3078918594707

Offset

0,3

Links

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

Wikipedia, Motzkin number

Formula

a(n) = A001006(n) + A333498(n).

Maple

b:= proc(x, y, h) option remember; `if`(x=0, h+1, add(
      b(x-1, y+j, max(h, y)), j=-min(1, y)..min(1, x-y-1)))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..35);

Crossrefs

Row sums of A372014.

Cf. A001006, A261003, A333498.

Sequence in context: A059512 A094297 A026107 * A173765 A027969 A027971

Adjacent sequences: A372030 A372031 A372032 * A372034 A372035 A372036

Keyword

nonn

Author

Alois P. Heinz, Apr 16 2024

Status

approved