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A278393
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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 {-4,-3,-2,-1,0,1,2,3,4}.
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6
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1, 4, 26, 194, 1521, 12289, 101205, 844711, 7120398, 60477913, 516774114, 4437360897, 38256405777, 330948944639, 2871299293535, 24973776734091, 217690276938940, 1901204163460913, 16632544424086901, 145730139895667887, 1278596503973570665, 11231908572986043199
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OFFSET
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0,2
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COMMENTS
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By convention, the empty walk (corresponding to n=0) is considered to be a positive meander.
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LINKS
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MATHEMATICA
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frac[ex_] := Select[ex, Exponent[#, x] < 0&];
seq[n_] := Module[{v, m, p}, v = Table[0, n]; m = Sum[x^i, {i, -4, 4}]; 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];
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PROG
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(PARI) seq(n)={my(v=vector(n), m=sum(i=-4, 4, 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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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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