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A175891 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. 2
1, 1, 5, 29, 185, 1226, 8553, 61642, 455337, 3429002, 26229691, 203237747, 1591820564, 12582288455, 100241042348, 804090987555, 6488942266564, 52644171729304, 429123506792664, 3512829202462126, 28866426741057006, 238031465396515626, 1969001793889730276 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

MAPLE

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):

seq(a(n), n=0..35);  # Alois P. Heinz, May 16 2017

CROSSREFS

Cf. A000103, A122951, A175883, A286918.

Sequence in context: A194723 A190917 A153391 * A081336 A127846 A059231

Adjacent sequences:  A175888 A175889 A175890 * A175892 A175893 A175894

KEYWORD

nonn

AUTHOR

Eric Werley, Dec 05 2010

STATUS

approved

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Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)