A weighted extension of Fibonacci numbers
arXiv:2301.08016
Abstract
We extend Fibonacci numbers with arbitrary weights and generalize a dozen Fibonacci identities. As a special case, we propose an elliptic extension which extends the -Fibonacci polynomials appearing in Schur's work. The proofs of most of the identities are combinatorial, extending the proofs given by Benjamin and Quinn, and in the case, by Garrett. Some identities are proved by telescoping.
14 pages, comments solicited