Project Euler 321 - Swapping Counters

Official link: https://projecteuler.net/problem=321

Thought Process

Pen and paper gave me M(1) = 3, M(2) = 8, and we know M(3) = 15, with this I found https://oeis.org/A005563 and it has a description "This is also the number of moves that it takes n frogs to swap places with n toads on a strip of 2n + 1 squares (or positions, or lily pads) where a move is a single slide or jump" which is exactly our problem more commonly known as Toads and Frogs Problem.

The sequence gives us the following:

Interactive Code

Enter a number (yourinput)

Code will output the sum of the first yourinput terms