[seqfan] Re: Counting permutations
charles.greathouse at case.edu
Fri Nov 4 18:52:09 CET 2011
Orderless, no repeats allowed. Just the sum of the number of
partitions of n with greatest part exactly k for k = 1..m.
Case Western Reserve University
On Fri, Nov 4, 2011 at 1:21 PM, wouter meeussen
<wouter.meeussen at pandora.be> wrote:
> I agree that 2-dim arrays are hard to search.
> As to your main question,
> p(n,m) ways to choose numbers from 1 .. m with sum *exactly* n
> looks like the partitions of n with largest part <=m.
> But you didn't specify if the "ways to choose" are ordered or orderless,
> nor if repeats are allowed or not.
> Could you clarify with an example?
> ----- Original Message -----
> From: "Charles Greathouse" <charles.greathouse at case.edu>
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Sent: Friday, November 04, 2011 5:53 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
>> Case Western Reserve University
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