OFFSET
0,4
COMMENTS
A peakless Motzkin path of length n is a lattice path from (0,0) to (n,0) using only steps U = (1,1), F = (1,0) and D = (1,-1) but no consecutive steps UD.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..555
Wikipedia, Motzkin number
FORMULA
a(n) == 1 (mod n) for n>=1.
MAPLE
b:= proc(x, y, t, k) option remember; `if`(y<0 or y>x, 0,
`if`(x=0, 1, k*b(x-1, y+1, true, k)+b(x-1, y, false, k)+
`if`(t, 0, b(x-1, y-1, false, k))))
end:
a:= n-> b(n, 0, false, n):
seq(a(n), n=0..24);
CROSSREFS
KEYWORD
nonn,new
AUTHOR
Alois P. Heinz, Apr 12 2026
STATUS
approved