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A278392 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 {-3,-2,-1,0,1,2,3}. 6
1, 3, 15, 87, 530, 3329, 21316, 138345, 906853, 5989967, 39804817, 265812731, 1782288408, 11991201709, 80911836411, 547334588037, 3710610424765, 25204313298581, 171492983631249, 1168638213247713, 7974592724571446, 54484621312318007, 372671912259214487 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

By convention, the empty walk (corresponding to n=0) is considered to be a positive meander.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, D. Nguyen, and M. Wallner, Explicit formulas for enumeration of lattice paths: basketball and the kernel method, arXiv:1609.06473 [math.CO], 2016.

MATHEMATICA

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

seq[n_] := Module[{v, m, p}, v = Table[0, n]; m = Sum[x^i, {i, -3, 3}]; 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[23] (* Jean-Fran├žois Alcover, Jul 01 2018, after Andrew Howroyd *)

PROG

(PARI) seq(n)={my(v=vector(n), m=sum(i=-3, 3, 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

CROSSREFS

Cf. A276852, A278391, A278393, A278394, A278395, A278396, A278398.

Sequence in context: A220875 A075841 A152596 * A168503 A089022 A246538

Adjacent sequences:  A278389 A278390 A278391 * A278393 A278394 A278395

KEYWORD

nonn,walk

AUTHOR

David Nguyen, Nov 20 2016

STATUS

approved

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Last modified November 12 07:16 EST 2019. Contains 329052 sequences. (Running on oeis4.)