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Transformations of Integer Sequences

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.

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