login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A225041 Number of 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), H=(1,0) and S=(0,1). 5
1, 1, 3, 9, 35, 145, 659, 3137, 15619, 80177, 422595, 2273633, 12447667, 69138193, 388784259, 2209440945, 12671782579, 73260414481, 426545078627, 2499059841249, 14723542302627, 87181150961361, 518554078448339, 3097007445391441, 18565515801339827 (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 * (3+2*sqrt(3))^n / n^(3/2), where c = 0.05641378816540215191327201376... . - Vaclav Kotesovec, Sep 07 2014

EXAMPLE

a(0) = 1: the empty path.

a(1) = 1: H.

a(2) = 3: HH, UD, HSD.

a(3) = 9: HHH, UDH, HSDH, UHD, HSHD, HUD, HHSD, UDSD, HSDSD.

MAPLE

b:= proc(x, y) option remember; `if`(y>x, 0, `if`(x=0, 1,

       b(x-1, y)+`if`(y>0, b(x-1, y-1)+b(x, y-1), 0)+b(x-1, y+1)))

    end:

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

seq(a(n), n=0..25);

MATHEMATICA

b[x_, y_] := b[x, y] = If[y>x, 0, If[x==0, 1, b[x-1, y]+If[y>0, b[x-1, y-1] + b[x, y-1], 0] + b[x-1, y+1]]];

a[n_] := b[n, 0];

Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Mar 29 2017, translated from Maple *)

CROSSREFS

Cf. A001006 (without S-steps), A114296 (without U-steps), A198324 (without H-steps), A225042 (paths to (n,n)), A286760.

Sequence in context: A102865 A046697 A151045 * A074507 A217924 A030268

Adjacent sequences:  A225038 A225039 A225040 * A225042 A225043 A225044

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 25 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 21 00:49 EDT 2019. Contains 325189 sequences. (Running on oeis4.)