Transformations of Integer Sequences

Transformations of Integer Sequences

A subpage of the The On-Line Encyclopedia of Integer Sequences, which makes extensive use of these transformations.

Keywords: AND-convolution, binomial, bisect, boustrophedon, complement, convolution, decimate, differences, Euler, exponential, inverse, Lambert, lcm-convolution, logarithmic, Moebius (or Mobius), OR-convolution, partial products, partial sums, partition, revert (or reversion), sort, trisect, XOR-convolution, weigh, etc., transforms; Maple, Mathematica, PARI.

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This page has links to four other web pages which give procedures for performing a large number of useful transformations on sequences and numbers. The programs

• Maple programs.
• Mathematica programs, written by Olivier Gerard.
• PARI programs, written by Christian G. Bower.
• See also the description of some further transforms written by Christian G. Bower.

References

• M. Bernstein & N. J. A. Sloane, Some canonical sequences of integers, Linear Algebra and its Applications, 226-228 (1995), 57-72.
• P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102.
• J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Comb. Theory, 17A 44-54 1996.
• N. J. A. Sloane and S. Plouffe, The Encyclopedia of Integer Sequences, Academic Press, San Diego, 1995, especially Section 2.7.