<p>Yes and no. As already observed, there are an infinite number of possible answers. However, it is possible to check certain types of generator to see whether they're capable of explaining the known values.</p>

<p>E.g. polynomials can be tested by looking at nth differences. Other types of generator can be tested by treating the sequence as coefficients of a generating function and looking at nth derivatives of that g.f.</p>

<p>See the description of the <a href="https://oeis.org/demos.html" rel="nofollow">OEIS Superseeker</a> for a brief discussion of some relevant ideas, and check out the academic literature (RATE, GFUN, <a href="http://arxiv.org/abs/math/0702086" rel="nofollow">extensions</a>).</p>
Identify generator type given resulting sequence only
<p>Not sure how realistic this is, but anyway, say, I have sequence of some numbers : </p>

<pre><code>1, 1, 2, 3, 5, 8, 13, 21
</code></pre>

<p>I am a human and for me it is obvious that this is Fibonacci sequence.</p>

<p><strong>Question :</strong> is there some programmatic way to determine nature of the generator that created this sequence and generate next value in this sequence? Is it possible to determine formula that was used to generate selected sequence, at least with some approximation?</p>