cp's OEIS Frontend

A278391 Number of positive meanders (walks starting at the origin and ending at any altitude > 0 that never touch or go below the x-axis in between) with n steps from {-2,-1,0,1,2}.

%I A278391 #27 Jun 30 2018 16:20:28
%S A278391 1,2,7,29,126,565,2583,11971,56038,264345,1254579,5983628,28655047,
%T A278391 137697549,663621741,3206344672,15525816066,75324830665,366071485943,
%U A278391 1781794374016,8684511754535,42381025041490,207055067487165,1012617403658500,4956924278927910
%N A278391 Number of positive meanders (walks starting at the origin and ending at any altitude > 0 that never touch or go below the x-axis in between) with n steps from {-2,-1,0,1,2}.
%C A278391 By convention, the empty walk (corresponding to n=0) is considered to be a positive meander.
%H A278391 Andrew Howroyd, <a href="/A278391/b278391.txt">Table of n, a(n) for n = 0..200</a>
%H A278391 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:1609.06473 [math.CO], 2016.
%t A278391 frac[ex_] := Select[ex, Exponent[#, x] < 0&];
%t A278391 seq[n_] := Module[{v, m, p}, v = Table[0, n]; m = Sum[x^i, {i, -2, 2}]; p = 1/x; v[[1]] = 1; For[i = 2, i <= n, i++, p = p*m // Expand; p = p - frac[p]; v[[i]] = p /. x -> 1]; v];
%t A278391 seq[25] (* _Jean-François Alcover_, Jun 30 2018, after _Andrew Howroyd_ *)
%o A278391 (PARI) seq(n)={my(v=vector(n), m=sum(i=-2, 2, x^i), p=1/x); v[1]=1; for(i=2, n, p*=m; p-=frac(p); v[i]=subst(p,x,1)); v} \\ _Andrew Howroyd_, Jun 27 2018
%Y A278391 Cf. A276903, A278392, A278393, A278394, A278395, A278396, A278398.
%K A278391 nonn,walk
%O A278391 0,2
%A A278391 _David Nguyen_, Nov 20 2016