New Binomial Identities for Fibonacci, Lucas, and Generalized Fibonacci Sequences with Multiple Indices
Abstract
This paper presents new identities expressing the terms of Fibonacci, Lucas, and generalized Fibonacci sequences with multiple indices through powers of Lucas numbers and binomial coefficients. The obtained formulas rely on the application of symmetric polynomials (Waring's formulas) to the classical Binet's formula. Particular attention is given to the binomial expansion for the generalized Fibonacci sequence, which structurally combines two adjacent binomial coefficients from Pascal's triangle.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Advanced Combinatorial Mathematics
Advanced Mathematical Identities
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 12 March 2026
- Language
- EN
- Document type
- Preprint