The FibonacciFubini and LucasFubini numbers
Abstract
Based on the combinatorial interpretation of the ordered Bell numbers, which count all the ordered partitions of the set $[n]=\{1,2,\dots,n\}$, we introduce the Fibonacci partition as a Fibonacci permutation of its blocks. Then we define the FibonacciFubini numbers that count the total number of Fibonacci partitions of $[n]$. We study the classical properties of this sequence (generating function, explicit and Dobińskilike formula, etc.), we give combinatorial interpretation, and we extensively examine the FibonacciFubini 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2024
 DOI:
 10.48550/arXiv.2407.04409
 arXiv:
 arXiv:2407.04409
 Bibcode:
 2024arXiv240704409D
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Number Theory;
 05A15;
 05A18;
 11B39;
 11B37;
 11B73
 EPrint:
 18 pages, 3 figures, 3 tables