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A333106 Total number of nodes summed over all nonnegative lattice paths from (0,0) to (n,0) where the allowed steps at (x,y) are (1,v) with v in {-1,0,...,max(y,1)}. 5
1, 2, 6, 16, 45, 126, 357, 1024, 2979, 8800, 26422, 80688, 250705, 792568, 2548620, 8331568, 27667109, 93241152, 318569656, 1102246040, 3857916552, 13644697000, 48716177272, 175417870080, 636493447625, 2325399611652, 8548381939932, 31599848465276 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1668

Wikipedia, Counting lattice paths

Wikipedia, Motzkin number

MAPLE

b:= proc(x, y) option remember; `if`(x=0, 1, add(

      b(x-1, y+j), j=-min(1, y)..min(max(1, y), x-y-1)))

    end:

a:= n-> (n+1)*b(n, 0):

seq(a(n), n=0..29);

CROSSREFS

Cf. A333070, A333105, A333107, A333608.

Sequence in context: A126285 A026163 A005717 * A025266 A074403 A337318

Adjacent sequences:  A333103 A333104 A333105 * A333107 A333108 A333109

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 07 2020

STATUS

approved

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Last modified January 23 14:45 EST 2021. Contains 340385 sequences. (Running on oeis4.)