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A306813 Number of 2n-step paths from (0,0) to (0,n) that stay in the first quadrant (but may touch the axes) consisting of steps (-1,0), (0,1), (0,-1) and (1,-1). 3
1, 0, 3, 10, 20, 237, 770, 3944, 28635, 112360, 744084, 4381083, 21579779, 143815322, 801165187, 4578481584, 29176623983, 165772480380, 1013147794546, 6259309820475, 36974951346176, 230752749518819, 1413352914731005, 8618746801792237, 53986291171211635 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1116 (terms 0..500 from Alois P. Heinz)

FORMULA

a(n) = A306814(2n,n).

a(n) ~ c * d^n / n^2, where d = 6.7004802541941947450873... and c = 0.5171899701803656646... - Vaclav Kotesovec, Apr 13 2019

EXAMPLE

a(0) = 1: [(0,0)].

a(2) = 3:

  [(0,0), (0,1), (0,0), (0,1), (0,2)],

  [(0,0), (0,1), (0,2), (0,1), (0,2)],

  [(0,0), (0,1), (0,2), (0,3), (0,2)].

a(3) = 10:

  [(0,0), (0,1), (1,0), (1,1), (1,2), (1,3), (0,3)],

  [(0,0), (0,1), (0,2), (1,1), (1,2), (1,3), (0,3)],

  [(0,0), (0,1), (0,2), (0,3), (1,2), (1,3), (0,3)],

  [(0,0), (0,1), (0,2), (0,3), (0,4), (1,3), (0,3)],

  [(0,0), (0,1), (1,0), (1,1), (1,2), (0,2), (0,3)],

  [(0,0), (0,1), (0,2), (1,1), (1,2), (0,2), (0,3)],

  [(0,0), (0,1), (0,2), (0,3), (1,2), (0,2), (0,3)],

  [(0,0), (0,1), (1,0), (1,1), (0,1), (0,2), (0,3)],

  [(0,0), (0,1), (0,2), (1,1), (0,1), (0,2), (0,3)],

  [(0,0), (0,1), (1,0), (0,0), (0,1), (0,2), (0,3)].

MAPLE

b:= proc(n, x, y) option remember; `if`(min(n, x, y, n-x-y)<0, 0,

      `if`(n=0, 1, add(b(n-1, x-d[1], y-d[2]),

       d=[[-1, 0], [0, 1], [0, -1], [1, -1]])))

    end:

a:= n-> b(2*n, 0, n):

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

CROSSREFS

Cf. A000108, A126596, A174687, A306814, A317782.

Sequence in context: A213850 A081205 A273379 * A092305 A196166 A073604

Adjacent sequences:  A306810 A306811 A306812 * A306814 A306815 A306816

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Mar 11 2019

STATUS

approved

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Last modified January 26 11:13 EST 2020. Contains 331279 sequences. (Running on oeis4.)