[Math] Find the next two terms in this sequence.

sequences-and-series

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.

Best Answer

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 http://oeis.org/A056520).

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