The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A278391 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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}.
(history; published version)

#27 by Alois P. Heinz at Sat Jun 30 16:20:28 EDT 2018

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proposed

approved

#26 by Jean-François Alcover at Sat Jun 30 16:18:27 EDT 2018

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editing

proposed

#25 by Jean-François Alcover at Sat Jun 30 16:18:23 EDT 2018

MATHEMATICA

frac[ex_] := Select[ex, Exponent[#, x] < 0&];

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];

seq[25] (* Jean-François Alcover, Jun 30 2018, after Andrew Howroyd *)

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approved

editing

#24 by Bruno Berselli at Thu Jun 28 04:50:32 EDT 2018

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reviewed

approved

#23 by Joerg Arndt at Thu Jun 28 04:10:46 EDT 2018

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proposed

reviewed

#22 by Andrew Howroyd at Wed Jun 27 19:16:50 EDT 2018

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editing

proposed

#21 by Andrew Howroyd at Wed Jun 27 18:44:52 EDT 2018

LINKS

Andrew Howroyd, <a href="/A278391/b278391.txt">Table of n, a(n) for n = 0..200</a>

PROG

(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

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approved

editing

#20 by Alois P. Heinz at Tue Nov 22 17:17:30 EST 2016

STATUS

editing

approved

#19 by Alois P. Heinz at Tue Nov 22 17:17:27 EST 2016

LINKS

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.

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approved

editing

#18 by Charles R Greathouse IV at Mon Nov 21 15:06:28 EST 2016

STATUS

proposed

approved