cp's OEIS Frontend

A278394 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,-1,1,2}.

%I A278394 #26 Jul 01 2018 08:38:05
%S A278394 1,2,5,17,58,209,761,2823,10557,39833,151147,576564,2208163,8486987,
%T A278394 32714813,126430229,489685674,1900350201,7387530575,28763059410,
%U A278394 112142791763,437774109384,1710883748796,6693281604018,26210038447737,102724200946467,402925631267151
%N A278394 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,-1,1,2}.
%C A278394 By convention, the empty walk (corresponding to n=0) is considered to be a positive meander.
%H A278394 Andrew Howroyd, <a href="/A278394/b278394.txt">Table of n, a(n) for n = 0..200</a>
%H A278394 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 A278394 frac[ex_] := Select[ex, Exponent[#, x] < 0&];
%t A278394 seq[n_] := Module[{v, m, p}, v = Table[0, n]; m = Sum[x^i, {i, -2, 2}] - 1; 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 A278394 seq[27] (* _Jean-François Alcover_, Jul 01 2018, after _Andrew Howroyd_ *)
%o A278394 (PARI) seq(n)={my(v=vector(n), m=sum(i=-2, 2, x^i)-1, 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 A278394 Cf. A276852, A278391, A278392, A278393, A278395, A278396, A278398.
%K A278394 nonn,walk
%O A278394 0,2
%A A278394 _David Nguyen_, Nov 20 2016