Find the next two terms in this sequence.

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The first five numbers of the sequence are the following ones:

1, 2, 6, 15, 31, ..., ...

Target: What I would like to know is the general formula of the sequence.

Solution: The numbers are 56 and 92.

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2 Answers

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The $(n+1)^\text{th}$ term of the sequence is given by: \begin{equation} \frac{(n+2)(2n^2-n+3)}{6}. \end{equation}

This is sequence number A056520 on the Online Encyclopedia of Integer Sequences (see ).

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HINT: The sequence is given by $a_n=a_{n-1}+(n-1)^2$

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