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Has anyone seen the relation $$ nP_{2}(n)=P_{3}(n-1)+\sum_{i=1}^ni^2 $$ where $P_2(n)$ is the $n$th triangular number and $P_3(n)$ is the $n$th tetrahedral number?

I know the straightforward algebra proof, and I have the geometric proof, but I was wondering where, if at all, this may have been in the literature? Thanks.

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closed as off-topic by Isaac Browne, Namaste, Shailesh, Xander Henderson, user21820 Jul 2 '18 at 9:46

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To strictly answer where this may have been in the literature, the answer is without a doubt The On-Line Encyclopedia of Integer Sequences.

There are a lot of formulas there, a good chance yours is a transformation of one of them.

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