On the coefficients of a Fibonacci power series

2001/10/16 by Federico Ardila M, M, Federico Ardila
Mathematics · Physics and Astronomy · #05A17 #11B39 #11P81 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A17 #msc:11B39 #msc:11P81

paper · pdf · doi:10.48550/arxiv.math/0110160

3 pages

arxiv created 2001/10/16 · openalex publication_date 2001/10/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit description of the coefficients of the formal power series (1-x)(1-x²)(1-x³)(1-x⁵)(1-x⁸)(1-x¹3)... In particular, we show that all the coefficients are equal to -1, 0 or 1.

Related

• The coefficients of a Fibonacci power series
• Some power series extensions of Fibonacci and Lucas polynomials
• Generalized Fibonacci polynomials and Fibonomial coefficients
• One level summations for powers of Fibonacci and Lucas polynomials
• Power Fibonacci Sequences