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A276901 Number of positive walks with n steps {-3,-2,-1,1,2,3} starting at the origin, ending at altitude 2, and staying strictly above the x-axis. 10
0, 1, 2, 9, 34, 159, 730, 3579, 17762, 90538, 467796, 2452727, 12997554, 69549847, 375159290, 2038068813, 11140256754, 61227097438, 338140106124, 1875581756078, 10444142352812, 58364192607047, 327203347219250, 1839778650617309, 10372512509521074 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1291

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}] + Sum[walks[n - 1, k + x, h], {x, h}];

(* walks represents the number of positive walks with n steps {-h, -h+1, ... -1, 1, ..., h} that end at altitude k *)

A276901[n_] := (Do[walks[m, k, 3], {m, n}, {k, 3 m}]; walks[n, 2, 3]) (* Davin Park, Oct 10 2016 *)

CROSSREFS

Cf. A276852, A276902, A276903, A276904.

Sequence in context: A150942 A150943 A150944 * A151308 A215943 A140217

Adjacent sequences:  A276898 A276899 A276900 * A276902 A276903 A276904

KEYWORD

nonn,walk

AUTHOR

Michael Wallner, Sep 21 2016

STATUS

approved

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Last modified March 30 09:49 EDT 2020. Contains 333125 sequences. (Running on oeis4.)