Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.5

On the Periodicity Problem for Residual r-Fubini Sequences

Amir Abbas Asgari
National Organization for Development of Exceptional Talents (NODET)

Majid Jahangiri
School of Mathematics
Department of Science
Shahid Rajaee Teacher Training University
P. O. Box 16785-163


For any positive integer r, the r-Fubini number with parameter n, denoted by Fn,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.

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(Concerned with sequences A000670 A008277 A143494 A143495 A143496 A232472 A232473 A232474.)

Received March 18 2017; revised version received April 16 2017; April 1 2018; April 12 2018; April 21 2018. Published in Journal of Integer Sequences, May 8 2018.

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