Impulse Response Sequences and Construction of Number Sequence Identities

In this paper, we investigate impulse response sequences ov er the integers by pre-senting their generating functions and expressions. We also establish some of the corre-sponding identities. In addition, we give the relationship between an impulse response sequence and all linear recurring sequences satisfying the same linear recurrence rela- tion, 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 Boustro phedon transform.