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On the Periodicity Problem for Residual ***r*-Fubini Sequences

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Amir Abbas Asgari

National Organization for Development of Exceptional Talents (NODET)

Tehran

Iran

Majid Jahangiri

School of Mathematics

Department of Science

Shahid Rajaee Teacher Training University

P. O. Box 16785-163

Tehran

Iran

**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.

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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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