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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.

%I A276904 #28 Oct 11 2016 05:18:11
%S A276904 0,1,3,14,68,358,1966,11172,65104,387029,2337919,14309783,88555917,
%T A276904 553171371,3483277785,22087378303,140913963221,903876307075,
%U A276904 5825742149049,37710582868464,245052827645474,1598017940728401,10454217006683855,68591382498826168
%N 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.
%H A276904 Alois P. Heinz, <a href="/A276904/b276904.txt">Table of n, a(n) for n = 0..1189</a>
%H A276904 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 A276904 walks[n_, k_, h_] = 0;
%t A276904 walks[1, k_, h_] := Boole[0 < k <= h];
%t A276904 walks[n_, k_, h_] /; n >= 2 && k > 0 := walks[n, k, h] = Sum[walks[n - 1, k + x, h], {x, -h, h}];
%t A276904 (* walks represents the number of positive walks with n steps {-h, -h+1, ... , h} that end at altitude k *)
%t A276904 A276904[n_] := (Do[walks[m, k, 3], {m, n}, {k, 3 m}]; walks[n, 2, 3]) (* _Davin Park_, Oct 10 2016 *)
%Y A276904 Cf. A276852, A276901, A276902, A276903.
%K A276904 nonn,walk
%O A276904 0,3
%A A276904 _Michael Wallner_, Sep 21 2016
%E A276904 More terms from _Alois P. Heinz_, Oct 10 2016