Keywords: AND-convolution, BINOMIAL transform, BINOMIALi transform, BISECT, boustrophedon transform, characteristic function, complement of sequence, compose two sequences, functional square root, continuant transform, convolution transform, inverse convolution transform, decimate, first differences, DIGREV = reverse digits, DIGSUM = sum of digits, Dirichlet convolution, Euler transform, Euleri transform, exponential transform, exponential convolution, GCD-convolution, Hankel transform, inverse of permutation, INVERT transform, INVERTi transform, LAH transform, LAHi transform, Lambert function, LCM-convolution, little Hankel transform. logarithmic transform, MOEBIUS transform, MOBIUS transform, MOEBIUSi transform, MOBIUSi transform, OR-convolution, partial products, partial sums, PARTITION transform, PARTITIONi transform, RECORDS transform, revert (or reversion), REVEGF = reversion of e.g.f., SERIESTOLISTDIV, SERIESTOLISTMULT, SERIESTOSERIESDIV, SERIESTOSERIESMULT, SERIES2, SERIES2TOLIST, SERIES2TOLISTMULT, SERIES2HTOLIST, SERIES2HTOLISTMULT, sort, STIRLING transform, STIRLINGi transform, Stirling-Bernoulli transform, SUPPORT transform, trisect, XOR-convolution, WEIGH transform, 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.