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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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    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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The answer is ambiguous for example you could take $9 (200 + x (16 x -111))$ or $3 x (37 + x (5 x - 27))$ which can be found by solving the interpolation problem (those are the easy ones with low degree). There are also programs that can make some guesses for the generating sequence but they will not be happy if you feed them only 3 points.

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    Thank you very much for the explanation. I am obviously coming from a different background, so I appreciate that you all even looked at my question.2011-05-05