Robert Dougherty Bliss, Rutgers University

Abstract

The Fibonacci numbers F(n) satisfy the famous recurrence F(n + 2) = F(n + 1) + F(n). The "C-finite ansatz" tells us that the family of sequences F(2n), F(3n), F(4n), ..., along with their sums and products satisfy similar recurrences. However, even more is true. We will show that the recurrences satisfied by F(n*i) and F(n*i) * F(n*j), for any C-finite sequence F, satisfy meta recurrences which lead to generating function and summation identities.

Link to video: https://vimeo.com/700914615

Presented Via Zoom: https://rutgers.zoom.us/j/94346444480

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/