A summation formula for generalized k-bonacci numbers

2022/11/01 by Jean‐Christophe Pain, Pain, Jean-Christophe
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2211.00364

openalex publication_date 2022/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we present a simple summation formula for k-bonacci numbers. The derivation consists in obtaining the generating function of such numbers, and noting that its evaluation at a particular value yields a formula generalizing a known expression for Fibonacci numbers.

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• Sums of k-bonacci Numbers
• Connecting the Stirling numbers and k-bonacci sums
• Four New Generalized Fibonacci Number Summation Identities
• Formula for the nth k-Generalized Fibonacci-like Number
• Some applications of the Lagrange inversion formula for the k-Fibonacci numbers