How many unique ordered lists of $N$ integers - $(q_1, ..., q_N)$ - can I form if $q_i \in [0, M]$, and we have the restriction that $\sum_{i=0}^{N} q_i \geq k$?
The number of unique ordered sets of integers over some domain provided that the elements of the set sum to some at least some value $k$
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combinatorics
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0What is $Q$? Perhaps that should be removed, as well as "possible unique". – 2012-12-24
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0@leonbloy Q is an ordered set of integers, for example, when N=3, we have: {q1, q2, q3}. – 2012-12-24
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0@leonbloy I have made the requested changes. Hopefully this should be better? – 2012-12-24
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0Ok. Two more clarifications: the order must be strict? (no equal integers? in this case the problem could be stated in combinatoric terms). Second: the notation $q_i \in [0, M]$ is equivalent to $q_i= 0, 1\cdots M$? – 2012-12-24
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0@leonbloy Integers may be equal, however {10, 5} must be counted as distinct from {5, 10}, for example. Yes, regarding the second point. – 2012-12-24