An interesting series of numbers.

I discovered a interesting series of numbers, do tell me if you see the pattern in them.

1, 5, 13, 25,41,61,85, 113, …

The pattern is that the difference of any two terms is equal to a multiple of four.

Now, another challenge for you is to find the formula that generates the nth such number.

The formula is 1/2 {(2x+1)^2 + 1}

All these discoveries were made by me.

Thank you,

Nunghead