Some Canonical Sequences of Integers
Combinatorics
2007-07-16 v1 Information Theory
math.IT
Abstract
Extending earlier work of R. Donaghey and P. J. Cameron, we investigate some canonical "eigen-sequences" associated with transformations of integer sequences. Several known sequences appear in a new setting: for instance the sequences (such as 1, 3, 11, 49, 257, 1531, ...) studied by T. Tsuzuku, H. O. Foulkes and A. Kerber in connection with multiply transitive groups are eigen-sequences for the binomial transform. Many interesting new sequences also arise, such as 1, 1, 2, 26, 152, 1144, ..., which shifts one place left when transformed by the Stirling numbers of the second kind, and whose exponential generating function satisfies A'(x) = A(e^x -1) + 1.
Cite
@article{arxiv.math/0205301,
title = {Some Canonical Sequences of Integers},
author = {Mira Bernstein and N. J. A. Sloane},
journal= {arXiv preprint arXiv:math/0205301},
year = {2007}
}
Comments
18 pages, 2 figures; Dedicated to Professor J. J. Seidel