On the periodicity problem for residual \(r\)-Fubini sequences
Published in Journal of Integer Sequences, 2018
Abstract
For any positive integer \(r\), the \(r\)-Fubini number with parameter \(n\), denoted by \(F_{n,r}\), is equal to the number of ways that the elements of a set with \(n+r\) elements can be weakly ordered such that the \(r\) least elements are in distinct orders. In this article we focus on the sequence of residues of the \(r\)-Fubini numbers modulo an arbitrary positive integer \(s\) and show that this sequence is periodic and then, exhibit how to calculate its period length.
Recommended citation: Asgari, Amir Abbas and Jahangiri, Majid. On the periodicity problem for residual $r$-Fubini sequences. J. Integer Seq., vol. 21 (2018), no. 4, Art. 18.4.5, 16 pp.
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