If you want to look deeper into this, check out this paper (PDF warning) https://ir.library.oregonstate.edu/downloads/t435gg51w

Examples are given in Common Lisp at the end, which at least for me, is infinitely easier to read than mathematical notation.

My father independently discovers that Fibonacci numbers can be calculated with sum of binomial coefficients. I went online and find that it was already discovered in 19th century by Édouard Lucas :) His discovery is just as original as Lucas's.