I am studying number pyramids. He is a 3-Based Number Pyramid

8
3 5 It is constructec by each two bricks adding
1 2 3 together to make the next brick.

In this pyramid, Base Number=3
Starting Number=1
Finishing Number=8


Here is my formula for working out the Finishing Number for all pyramids with any Base Number.
2to the power of B-1 S + (B-1) 2to the power of B-2

To prove it works, we use it for the pyramid we have here. We come out with 4S+4...and we then realize that using 4S+4 we can get the finishing number for the pyramid!


What I cannot do is link this to binomial formula, but I know it's possible. If anyone knows, please tell me. Thanks a lot, have a nice day.