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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A227580 Number of lattice paths from {n}^3 to {0}^3 using steps that decrement one component such that for each point (p_1,p_2,p_3) we have p_1<=p_2<=p_3. 2
1, 1, 14, 290, 7680, 238636, 8285506, 312077474, 12509563082, 526701471002, 23076216957520, 1044813920439200, 48630132961189400, 2317337976558074760, 112689430179458971738, 5577655817793682738378, 280392321290875174774106, 14290804691034216155457274 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) ~ 2^(6*n+10)/(sqrt(3)*Pi*(5*n)^4). - Vaclav Kotesovec, Jul 18 2013

EXAMPLE

a(2) = 14: [(2,2,2),(0,2,2),(0,0,2),(0,0,0)], [(2,2,2),(0,2,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(0,2,2),(0,1,2),(0,0,2),(0,0,0)], [(2,2,2),(0,2,2),(0,1,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(0,2,2),(0,1,2),(0,1,1),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,0,2),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,1,2),(0,0,2),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,1,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,1,2),(0,1,1),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(1,1,2),(0,1,2),(0,0,2),(0,0,0)], [(2,2,2),(1,2,2),(1,1,2),(0,1,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(1,1,2),(0,1,2),(0,1,1),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(1,1,2),(1,1,1),(0,1,1),(0,0,1),(0,0,0)].

MAPLE

a:= proc(n) option remember; `if`(n<3, [1, 1, 14][n+1],

      ((n+1)*(665*n^3-1433*n^2+980*n-204) *a(n-1)

       -(n-2)*(1615*n^3-3218*n^2+1521*n-342) *a(n-2)

       +192*(5*n-1)*(n-3)*(n-2)^2 *a(n-3)) /

       (2*(n+2)*(5*n-6)*(n+1)^2))

    end:

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

CROSSREFS

Column k=3 of A227578.

Sequence in context: A259432 A233069 A181192 * A215869 A262740 A158475

Adjacent sequences:  A227577 A227578 A227579 * A227581 A227582 A227583

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 16 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 18 14:00 EDT 2018. Contains 315131 sequences. (Running on oeis4.)