#combinatorics

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meager oracle
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how many solutions does the ecuation d1 + d2 + ... + dk = n have, when di, with 1 <= i <= k, can be an integer from 0 to a given number X?

lofty coralBOT
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tough wadi
# meager oracle how many solutions does the ecuation d1 + d2 + ... + dk = n have, when di, with ...

This might help.
https://math.stackexchange.com/questions/553960/extended-stars-and-bars-problemwhere-the-upper-limit-of-the-variable-is-bounded

Mathematics Stack Exchange
Extended stars-and-bars problem(where the upper limit of the variab...

The problem of counting the solutions $(a_1,a_2,\ldots,a_n)$ with integer $a_i\geq0$ for $i\in{1,2,\ldots,n}$ such that
$$a_1+a_2+a_3+\ldots+a_n=N$$
can be solved with a stars-and-bars argument.
...

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Basically, when you have a lower limit for terms, it's easy. Not so easy with an upper limit, though.

meager oracle
meager oracle
tough wadi
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You're welcome!

meager oracle
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thx for the article ill have a look!!

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+close