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A276903 Number of positive walks with n steps {-2,-1,0,1,2} starting at the origin, ending at altitude 2, and staying strictly above the x-axis. 10
0, 1, 2, 7, 25, 96, 382, 1567, 6575, 28096, 121847, 534953, 2373032, 10619922, 47890013, 217395690, 992640367, 4555957948, 21007405327, 97266928685, 452046424465, 2108022305795, 9860773604035, 46256877824220, 217555982625385, 1025667805621986, 4846240583558277 (list; graph; refs; listen; history; text; internal format)
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

Cf. A276852, A276901, A276902, A276904.

Sequence in context: A150455 A150456 A150457 * A150458 A150459 A150460

Adjacent sequences:  A276900 A276901 A276902 * A276904 A276905 A276906

KEYWORD

nonn,walk

AUTHOR

Michael Wallner, Sep 21 2016

STATUS

approved

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Last modified April 9 10:32 EDT 2020. Contains 333348 sequences. (Running on oeis4.)