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A278416
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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 {-4,-3,-2,-1,1,2,3,4}.
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1
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1, 4, 26, 174, 1231, 8899, 65492, 487646, 3664123, 27723979, 210946444, 1612394958, 12371547879, 95230159650, 735060394986, 5687343753535, 44096482961189, 342530654187820, 2665058975987628, 20765913987073659, 162019898098364055, 1265622208055843635
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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seq[n_] := Module[{v = Table[1, n], m = Sum[ x^i, {i, -4, 4}] - 1, p = 1}, For[i = 2, i <= n, i++, p = Expand[p*m]; p = p - Select[p, Exponent[#, x] < 0&]; 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)-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
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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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