Set up a summation notation from a sequence

Question

I want to set up a summation notation for numbers of blocks that is needed in a podium with n layers but I dont know how to do that.

I calculated the following sequence: first layer: 9 blocks second layer: 16 block third layer: 25 blocks forth layer: 36 blocks

From first layer to second layer 7 more blocks is added, second layer to third layer 9 more blocks is added, third layer to forth layer 11 blocks is added and so on.

I also came up with the recursive formula: a(n) = a(n-1) + (a(n-1) - a(n-2)) + 2 (but I dont know if that will help me)

Answer 1

Consecutive odd numbers do add up to perfect squares so for a strict sum you could try:

$\displaystyle \sum_{k=0}^{n+2} (2k-1)$

The thing in brackets ensures the first layer has nine blocks. It's like I shifted the actual thing to remain between 0 and n