A080169

[Rob Pratt]

On Tue, 4 Feb 2003, Jens Voss wrote:

> The definition of the new sequence A080169 reads:
>
> > ID Number: A080169
> > Sequence:  1,3,13,81,541
> > Name:      Ways n competitors can rank in a competition, allowing for the
> >               possibility of ties.
> > Example:   Three competitors can finish in 13 ways: 1,2,3; 1,3,2; 2,1,3; 2,3,1;
> >               3,1,2; 3,2,1; 1,1,3; 2,2,1; 1,3,1; 2,1,2; 3,1,1; 1,2,2; 1,1,1.
> > Keywords:  more,nonn,new
> > Offset:    1
> > Author(s): Robert Lozyniak (nothing at example.com), Feb 04 2003
>
> Either I misunderstood this, or I can't count or there's a mistake:
> I am getting only 75 for a(4):
>
>  The  1 way of all four coming in first,
>  the  8 ways of having three come in simultaneously and one separately,
>  the  6 ways of having two pairs,
>  the 36 ways of having one pair and two separate competitors as well as
>  the 24 ways of all four coming in separately
> -------
> sum: 75
>
> Which ones did I miss?
>
> Regards,
> Jens


You didn't miss any.  This sequence is already in the database as A000670.


Rob Pratt
Department of Operations Research
The University of North Carolina at Chapel Hill

rpratt at email.unc.edu

http://www.unc.edu/~rpratt/