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A175891
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Number of lattice paths from (0,0) to (n,n) using steps S={(k,0),(0,k)|0<k<=4} which never go above the line y=x.
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2
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1, 1, 5, 29, 185, 1226, 8553, 61642, 455337, 3429002, 26229691, 203237747, 1591820564, 12582288455, 100241042348, 804090987555, 6488942266564, 52644171729304, 429123506792664, 3512829202462126, 28866426741057006, 238031465396515626, 1969001793889730276
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ c * d^n / n^(3/2), where d = 8.84734830841870961487278801886633962039798... is the real root of the equation 4 + 4*d - 8*d^2 - 8*d^3 + d^4 = 0 and c = 0.31736815701423989167651891084531024477617724724822148387263881713... - Vaclav Kotesovec, May 30 2017
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MAPLE
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b:= proc(x, y) option remember; `if`(y>x or y<0, 0,
`if`(x=0, 1, add(b(x-j, y)+b(x, y-j), j=1..4)))
end:
a:= n-> b(n$2):
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MATHEMATICA
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b[x_, y_] := b[x, y] = If[y > x || y < 0, 0, If[x == 0, 1, Sum[b[x - j, y] + b[x, y - j], {j, 1, 4}]]];
a[n_] := b[n, n];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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