# [seqfan] Re: Counting permutations

Ron Hardin rhhardin at att.net
Sat Nov 5 00:43:24 CET 2011

```I have a computation cooking since Oct 31 but not finished that starts
\$ cat tabstarts
Table starts
..1..1..1..1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1
..2..2..2..2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2
..3..2..2..2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2
..5..4..3..3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3..
..7..4..4..3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3....
.11..7..5..5.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4......
.15..8..6..5.5.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4........
.22.12..9..7.6.6.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5..........
.30.14.10..8.7.6.6.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5............
.42.21.13.11.9.8.7.7.6.6.6.6.6.6.6.6.6.6.6.6.6.6.6.6.6.6.6.6.6.6..............
\$ cat temp1000.txt
T(n,k)=Number of partitions of n+2k-2 with values >= k

rhhardin at mindspring.com
rhhardin at att.net (either)

----- Original Message ----
> From: Charles Greathouse <charles.greathouse at case.edu>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, November 4, 2011 12:53:47 PM
> Subject: [seqfan] Counting permutations
>
> I can't find a sequence that shows the number f(m, n) of ways to
> choose  numbers from 1, 2, ..., m with a sum of at most n.  Is this
> already in  the OEIS?  I tried searching for it as a triangle possibly
> missing some  columns, but couldn't find it.  I suppose it could also
> be thought of as  a rectangular array to be read by antidiagonals.
>
> (Generally it's hard to  search for two-dimensional entities in the
> OEIS; I wonder if there's a good  general solution.)
>
> Charles Greathouse
> Analyst/Programmer
> Case  Western Reserve  University
>
> _______________________________________________
>
> Seqfan  Mailing list - http://list.seqfan.eu/
>

```