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A286427
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Total number of nodes summed over all lattice paths from (0,0) to (n,0) that do not go below the x-axis or above the diagonal x=y and consist of steps U=(1,1), D=(1,-1) and S=(0,1).
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2
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1, 0, 3, 5, 24, 78, 325, 1272, 5373, 22572, 97762, 425716, 1882062, 8375064, 37601643, 169773435, 771096972, 3518065767, 16119884297, 74125225732, 341970676466, 1582133854847, 7338641255894, 34117910537671, 158946919835352, 741884929970516, 3468677541274922
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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 * 2^n * (1 + sqrt(2))^n / sqrt(n), where c = 0.0205249406642810706349830917137505197586781430984... - Vaclav Kotesovec, Sep 11 2021
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MAPLE
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b:= proc(x, y) option remember; `if`(y<0 or y>x, 0, `if`(x=0, [1$2],
(p-> p+[0, p[1]])(b(x, y-1)+b(x-1, y-1)+b(x-1, y+1))))
end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..30);
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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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