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I'm trying to find the common calculation between a series of numbers. For example:

2,4

3,9

4,16

I know that the calculation is simply the number squared. Another example would be:

3,18

4,52

5,110

In this example, I know that it is ((number * number) - 3) * number. So, with the number in the first set being 3, it would reduce down to ((3 * 3) - 3) * 3 = 18.

So, ultimately my question is trying to find the calculation between the following sets:

4,108

5,405

6,990

(for a bit of background as to why I'm asking this question, you can see my first failed attempt at asking the question here: https://math.stackexchange.com/questions/36689/finding-the-calculation-for-the-24th-permutation)

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    Apparently, you seem to know that a polynomial is generating your values from inputs (e.g. the second one applies the polynomial $x^3-3x$ to the integers). Lagrange interpolation can determine such a polynomial.2011-05-04
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    There are no simple answers for this kind of thing. Tell me what you want the "next" pair to be, I can find a rule that gives you all the pairs you have so far, and the one you want next. That rule will be given by a polynomial, so it won't even be ad hoc. See http://en.wikipedia.org/wiki/Lagrange_interpolation By the way, they aren't "sets", they aren't "sequences and series" either...2011-05-04
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    Thanks for the clarifications. In regard to the sequences statement, I agree that I'm not stating this very well. However, couldn't the sequence that I'm looking at be: 108,405,990,?2011-05-04
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    How do you know your second example is $(n^2-3)n$? It could just as easily be $12n^2-50n+60$, which has the advantage of involving only $n^2$, not $n^3$.2011-05-04

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