# Is it possible to guess n-th term of given number sequence?

Consider if we have number sequence e.g. $\left\{ 1, 6, 62, 344, ... \right\}$ I'd like to ask if is it possible to compute or estimate form of $n$-th element of this series.

Is it possible with Mathematica or maybe some math processes? I'll be glad for all hints and solution to this topic. Greetings,

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WolframAlpha can often guess, but it doesn't know anything about this. OEIS doesn't find it either – Cocopuffs Apr 12 '13 at 9:32
Where does the sequence come from? Any hint on how it is generated? With that, it might be possible to come up with a formula... – vonbrand Apr 12 '13 at 9:53
@vonbrand This example is "random". I need to design simulator that will count something and the output might be looking like this. I think we can consider that for all $n$ : $a_{n+1} > a_{n}$ and increasing speed will be faster than linear. – piotrdab Apr 12 '13 at 10:13
@Cocopuffs: I don't think WolframAlpha can generate series for $[\sqrt{n}]^2+n$? – Inceptio Apr 12 '13 at 10:21
@Inceptio It looks for "holonomic sequences", which has something to do with the generating power series satisfying a simple (polynomials) differential equation. It doesn't do everything, but it often helps. – Cocopuffs Apr 12 '13 at 10:48