Power Series Question

Hello,

I've been working on something that inspired me to use a specific number series and I do not know what this series is called.  I will explain/illustrate, so please bear with me:

For any consecutive integers, starting at 1 until any number greater than 1,

     if 3, 3^2 = 1 + 2 + 3 + 2 + 1

     if 6, 6^2 = 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1

I am using this for a specific application in finance, but would like to research its theoretical backing and other practical applications.

If anyone can help me out, thanks.

Danny