Gaurav Bhatnagar,
Archna Kumari, and
and Michael J. Schlosser
A weighted extension of Fibonacci numbers
(15 pages)
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 q-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 q-case,
by Garrett. Some identities are proved by telescoping.
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