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.


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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Namaste, Shailesh, Xander Henderson, user21820
If this question can be reworded to fit the rules in the help center, please edit the question.


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.


Not the answer you're looking for? Browse other questions tagged or ask your own question.