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I need some help to figure out the following number pattern:

Find the next number in the following sequence: $3, 2, 3, 12, 35, 78$.

I tired to figure out the difference by add/subtract/multiple/division also tried to find the existing known pattern still could not work it out.

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    $\begingroup$ According to OEIS, this sequence is not listed. $\endgroup$ – Euler....IS_ALIVE Nov 6 '13 at 4:34
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According to the Online Encyclopedia of Integer Sequences, this is the first 6 values of $n$ of the sequence $n^3 - 5n^2 + 7n$

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    $\begingroup$ Is this a contradiction to your comment? $\endgroup$ – BlackAdder Nov 6 '13 at 6:11
  • $\begingroup$ No. ${}{}{}{}{}{}$ $\endgroup$ – Euler....IS_ALIVE Nov 6 '13 at 6:55
  • $\begingroup$ so the next number is 147 = 7x7x7-5x7x7+7x7 $\endgroup$ – Karen Nov 6 '13 at 21:04
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183, because I say so.

(This makes it more than 30 characters, so there!)

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