OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1437
C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, D. Nguyen, and M. Wallner, Explicit formulas for enumeration of lattice paths: basketball and the kernel method, arXiv preprint arXiv:1609.06473 [math.CO], 2016.
MATHEMATICA
walks[n_, k_, h_] = 0;
walks[1, k_, h_] := Boole[0 < k <= h];
walks[n_, k_, h_] /; n >= 2 && k > 0 := walks[n, k, h] = Sum[walks[n - 1, k + x, h], {x, -h, h}];
(* walks represents the number of positive walks with n steps {-h, -h+1, ... , h} that end at altitude k *)
A276903[n_] := (Do[walks[m, k, 2], {m, n}, {k, 2 m}]; walks[n, 2, 2]) (* Davin Park, Oct 10 2016 *)
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Michael Wallner, Sep 21 2016
STATUS
approved