I need help with this problem.

Find a closed form solution for the following sequence 1,2,1,3,2,4,2,6,3,8,3,12


closed as off-topic by Batominovski, Hans Lundmark, user1551, Smylic, Shailesh May 2 '17 at 0:07

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  • $\begingroup$ I can't really identify what the sequence is supposed to be to begin with. $\endgroup$ – Mees de Vries May 1 '17 at 14:48
  • 5
    $\begingroup$ This works. $$\small a_n=\frac{239 n^{11}}{3628800} - \frac{941 n^{10}}{201600} + \frac{15121 n^9}{103680} - \frac{106627 n^8}{40320} + \frac{4142051 n^7}{134400} - \frac{6953329 n^6}{28800} + \frac{937219637 n^5}{725760} - \frac{189056173 n^4}{40320} + \frac{1457296303 n^3}{129600} - \frac{846796739 n^2}{50400} + \frac{35016917 n}{2520} - 4727$$ $\endgroup$ – projectilemotion May 1 '17 at 14:50

Seems to be of the form $1,2,1,3,\ldots,k,2^k,k,3\cdot 2^{k-1},\ldots$. However, there are infinitely many sequences with "reasonably good definitions" which start with a given finite subsequence. The sequence given by projectilemotion is a perfectly good one.


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