Consider the sequence:
Find both a recurrence and a closed form for this sequence.
I've done some research and found out that the majority of these (except 0) are "pentagonal numbers." We haven't learned about these yet, but further research did allow me to find a formula:
$A_n = ((3n^2)-n)/2$
That is the closed form for this sequence, correct? Could someone possibly lead me as to how to get to that equation?
In terms of a recurrence, I'm somewhat lost.