

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 xaxis.


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
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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



