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A286425 Total number of nodes summed over all lattice paths from (0,0) to (n,n) 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, 2, 8, 44, 285, 2028, 15338, 120960, 983108, 8172094, 69116592, 592590616, 5136777504, 44928712804, 395907022448, 3510622573064, 31296093794827, 280275392413204, 2520017580255461, 22736733105613548, 205767848345966976, 1867240544055742660 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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$2)[2]:

seq(a(n), n=0..30);

CROSSREFS

Cf. A224769.

Sequence in context: A141147 A201374 A120928 * A260879 A179489 A240165

Adjacent sequences:  A286422 A286423 A286424 * A286426 A286427 A286428

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 14 2017

STATUS

approved

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Last modified April 16 09:36 EDT 2021. Contains 343030 sequences. (Running on oeis4.)