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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.

%I A276901 #28 Oct 11 2016 15:48:48
%S A276901 0,1,2,9,34,159,730,3579,17762,90538,467796,2452727,12997554,69549847,
%T A276901 375159290,2038068813,11140256754,61227097438,338140106124,
%U A276901 1875581756078,10444142352812,58364192607047,327203347219250,1839778650617309,10372512509521074
%N 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.
%H A276901 Alois P. Heinz, <a href="/A276901/b276901.txt">Table of n, a(n) for n = 0..1291</a>
%H A276901 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 A276901 walks[n_, k_, h_] = 0;
%t A276901 walks[1, k_, h_] := Boole[0 < k <= h];
%t A276901 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}];
%t A276901 (* walks represents the number of positive walks with n steps {-h, -h+1, ... -1, 1, ..., h} that end at altitude k *)
%t A276901 A276901[n_] := (Do[walks[m, k, 3], {m, n}, {k, 3 m}]; walks[n, 2, 3]) (* _Davin Park_, Oct 10 2016 *)
%Y A276901 Cf. A276852, A276902, A276903, A276904.
%K A276901 nonn,walk
%O A276901 0,3
%A A276901 _Michael Wallner_, Sep 21 2016