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A372033
The total number of levels visited by all Motzkin paths of length n.
2
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
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.
Sequence in context: A059512 A094297 A026107 * A173765 A027969 A027971
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 16 2024
STATUS
approved