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A333106
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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)}.
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5
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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
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OFFSET
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0,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1668
Wikipedia, Counting lattice paths
Wikipedia, Motzkin number
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MAPLE
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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);
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CROSSREFS
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Cf. A333070, A333105, A333107, A333608.
Sequence in context: A126285 A026163 A005717 * A025266 A074403 A337318
Adjacent sequences: A333103 A333104 A333105 * A333107 A333108 A333109
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Mar 07 2020
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STATUS
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approved
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