%I #22 Oct 11 2016 08:42:00

%S 0,1,2,7,25,96,382,1567,6575,28096,121847,534953,2373032,10619922,

%T 47890013,217395690,992640367,4555957948,21007405327,97266928685,

%U 452046424465,2108022305795,9860773604035,46256877824220,217555982625385,1025667805621986,4846240583558277

%N 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.

%H Alois P. Heinz, <a href="/A276903/b276903.txt">Table of n, a(n) for n = 0..1437</a>

%H C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, D. Nguyen, and M. Wallner, <a href="https://arxiv.org/abs/1609.06473">Explicit formulas for enumeration of lattice paths: basketball and the kernel method</a>, arXiv preprint arXiv:1609.06473 [math.CO], 2016.

%t walks[n_, k_, h_] = 0;

%t walks[1, k_, h_] := Boole[0 < k <= h];

%t walks[n_, k_, h_] /; n >= 2 && k > 0 := walks[n, k, h] = Sum[walks[n - 1, k + x, h], {x, -h, h}];

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

%t A276903[n_] := (Do[walks[m, k, 2], {m, n}, {k, 2 m}]; walks[n, 2, 2]) (* _Davin Park_, Oct 10 2016 *)

%Y Cf. A276852, A276901, A276902, A276904.

%K nonn,walk

%O 0,3

%A _Michael Wallner_, Sep 21 2016