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A286427 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). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

MAPLE

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);

CROSSREFS

Cf. A198324.

Sequence in context: A275148 A336425 A230985 * A290509 A208800 A249935

Adjacent sequences:  A286424 A286425 A286426 * A286428 A286429 A286430

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 14 2017

STATUS

approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)