The Fibonacci-Fubini and Lucas-Fubini Numbers
Abstract
Based on the combinatorial interpretation of the ordered Bell numbers, which count all the ordered partitions of the set [n]={1,2,…,n}, we introduce the Fibonacci partition as a Fibonacci permutation of its blocks. Then we define the Fibonacci-Fubini numbers that count the total number of Fibonacci partitions of [n].We study the classical properties of this sequence (generating function, explicit and Dobiński-like formula, Mellin derivative representation, etc.), we give combinatorial interpretation, and we extensively examine the Fibonacci-Fubini arithmetic triangle. We give some associate linear recurrence sequences, where in some sequences the Stirling numbers of the first and second kinds appear as well.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Advanced Mathematical Identities
Mathematics and Applications
Publication details
- Journal / source
- The Fibonacci Quarterly
- Publisher
- Informa UK Limited
- Volume
- 64
- Issue
- 3
- Pages
- 428–446
- Publication date
- 23 June 2026
- Language
- EN