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URL: https://oeis.org/A278398

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A278398
Number of meanders (walks starting at the origin and ending at any altitude >= 0 that may touch but never go below the x-axis) with n steps from {-3,-2,-1,1,2,3}.
9
1, 3, 15, 75, 400, 2169, 11989, 66985, 377718, 2144290, 12240943, 70193305, 404029950, 2332989921, 13508237399, 78399357623, 455959701700, 2656652705422, 15504203678738, 90614205677898, 530288460288008, 3107012752773125, 18223934202102463, 106996319699099591
OFFSET
0,2
LINKS
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}] - 1; p = 1; v[[1]] = 1; For[i = 2, i <= n, i++, p = p*m // Expand; p = p - frac[p]; v[[i]] = p /. x -> 1]; v];
seq[24] (* Jean-François Alcover, Jul 01 2018, after Andrew Howroyd *)
PROG
(PARI) seq(n)={my(v=vector(n), m=sum(i=-3, 3, x^i)-1, p=1); 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
KEYWORD
nonn,walk
AUTHOR
David Nguyen, Nov 20 2016
STATUS
approved