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 A333680 Total number of nodes summed over all nonnegative lattice paths from (0,0) to (n,0) such that slopes of adjacent steps differ by at most one, assuming zero slope before and after the paths. 4
 1, 2, 3, 8, 20, 48, 112, 272, 666, 1690, 4367, 11436, 30147, 80248, 215550, 583456, 1588956, 4351806, 11979481, 33127440, 91982688, 256354098, 716879847, 2010919560, 5656813275, 15954441334, 45106324389, 127809023944, 362897750254, 1032389760540, 2942278599032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 Alois P. Heinz, Animation of A333647(9) = 169 paths with a(9) = 1690 nodes Wikipedia, Counting lattice paths FORMULA a(n) = (n+1) * A333647(n). MAPLE b:= proc(x, y, t) option remember; `if`(x=0, 1, add(       b(x-1, y+j, j), j=max(t-1, -y)..min(x*(x-1)/2-y, t+1)))     end: a:= n-> (n+1)*b(n, 0\$2): seq(a(n), n=0..36); MATHEMATICA b[x_, y_, t_] := b[x, y, t] = If[x == 0, 1, Sum[      b[x-1, y+j, j], {j, Max[t-1, -y], Min[x(x-1)/2-y, t+1]}]]; a[n_] := (n+1) b[n, 0, 0]; a /@ Range[0, 36] (* Jean-François Alcover, Apr 26 2021, after Alois P. Heinz *) CROSSREFS Cf. A333647, A333678, A333679. Sequence in context: A337281 A092031 A082914 * A254533 A095341 A167123 Adjacent sequences:  A333677 A333678 A333679 * A333681 A333682 A333683 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 01 2020 STATUS approved

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Last modified May 20 09:27 EDT 2022. Contains 353871 sequences. (Running on oeis4.)