[seqfan] Re: Counting permutations

wouter meeussen wouter.meeussen at pandora.be
Fri Nov 4 18:21:51 CET 2011

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
> Analyst/Programmer
> Case Western Reserve University

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