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A276904 Number of positive walks with n steps {-3,-2,-1,0,1,2,3} starting at the origin, ending at altitude 2, and staying strictly above the x-axis. 9
0, 1, 3, 14, 68, 358, 1966, 11172, 65104, 387029, 2337919, 14309783, 88555917, 553171371, 3483277785, 22087378303, 140913963221, 903876307075, 5825742149049, 37710582868464, 245052827645474, 1598017940728401, 10454217006683855, 68591382498826168 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1189

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 *)

A276904[n_] := (Do[walks[m, k, 3], {m, n}, {k, 3 m}]; walks[n, 2, 3]) (* Davin Park, Oct 10 2016 *)

CROSSREFS

Cf. A276852, A276901, A276902, A276903.

Sequence in context: A113140 A151324 A121185 * A199314 A190725 A151325

Adjacent sequences: A276901 A276902 A276903 * A276905 A276906 A276907

KEYWORD

nonn,walk

AUTHOR

Michael Wallner, Sep 21 2016

EXTENSIONS

More terms from Alois P. Heinz, Oct 10 2016

STATUS

approved

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Last modified December 4 19:07 EST 2022. Contains 358563 sequences. (Running on oeis4.)