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October 28th, 2010, 02:21 PM   #1
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very hard question

could someone help with this please,

Let k be a non-negative integer. How many distinct integer-valued vectors (n1, n2, . . . , nr) are there which satisfy both of the following constraints?

nj ?k for all j=1,2,...,r
and
n1 + n2 + + nr = n.
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