Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.2

Impulse Response Sequences and Construction of Number Sequence Identities

Tian-Xiao He
Department of Mathematics
Illinois Wesleyan University
Bloomington, IL 61702-2900


In this paper, we investigate impulse response sequences over the integers by presenting their generating functions and expressions. We also establish some of the corresponding identities. In addition, we give the relationship between an impulse response sequence and all linear recurring sequences satisfying the same linear recurrence relation, which can be used to transfer the identities among different sequences. Finally, we discuss some applications of impulse response sequences to the structure of Stirling numbers of the second kind, the Wythoff array, and the Boustrophedon transform.

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(Concerned with sequences A000073 A000078 A001591 A079262 A122189 A141036.)

Received March 27 2013; revised version received March 29 2013; June 21 2013; August 27 2013. Published in Journal of Integer Sequences, October 12 2013.

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