Journal of Integer Sequences, Vol. 13 (2010), Article 10.4.2

Multiple Binomial Transforms and Families of Integer Sequences

Jiaqiang Pan
School of Biomedical Engineering and Instrumental Science
Zhejiang University
Hangzhou 210027


Based on the multiple binomial transforms introduced in this paper, the n-fold generating and generated sequences of a given integer sequence can be defined and a family of this integer sequence can be constructed. The family sets form a partition of the set of integer sequences. Special attention is paid to the recurrent integer sequences, which are produced by some linear and homogeneous recurrence relations or difference equations. For the recurrent integer sequences, a distinct rule to construct their families is obtained based on the linear difference calculus.

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(Concerned with sequences A000004 A000007 A000012 A000045 A000073 A001906 A039834 A093131 A115390.)

Received October 24 2009; revised versions received March 8 2010; March 20 2010. Published in Journal of Integer Sequences, March 23 2010.

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