The funny thing about these *bonacci sequences is that as we reach infinity in these sequences, the ratio between two consecutive numbers approach a certain value that is characteristical for the sequence. For the Fibonacci sequence the ratio is the golden ratio, which is a root of the polynomial x²−x−1. For the Tribonacci sequence, the ratio in a root in the polynomial x³−x²−x−1. And for a Nbonacci, the ratio is a solution to xⁿ−xⁿ⁻¹−…x²−x−1. This is easy to prove. And as N approaches infinity, the ratio will approach 2.
