Re: sum over i+j+k==n

• To: mathgroup at smc.vnet.net
• Subject: [mg84447] Re: sum over i+j+k==n
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Mon, 24 Dec 2007 04:52:11 -0500 (EST)
• References: <fkla8k\$3v1\$1@smc.vnet.net>

```Jack Kennedy wrote:
> Hi All,
> I often find myself needing to sum over triples
> (or other tuples) like i,j,k where i+j+k=n. Is there
> a convenient way to write this in Mathematica?

You didn't mention exactly how do you wish to write n as a sum of three
numbers.  In Mathematica 6, the Combinatorica package has
IntegerPartitions[], which does it one way.  For example:

In[1]:= << Combinatorica`

In[2]:= IntegerPartitions[10, {3}]
Out[2]= {{8, 1, 1}, {7, 2, 1}, {6, 3, 1}, {6, 2, 2}, {5, 4, 1}, {5, 3,
2}, {4, 4, 2}, {4, 3, 3}}

(IIRC in earlier versions Combinatorica could be loaded with
<<DiscreteMath`Combinatorica`)

I hope this helps,
Szabolcs

```

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