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# Sequence transforms

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**Sequence transforms** are operations on a subset of the set of integer sequences. Informally, they are a way of creating a new sequence from an existing sequence.

- Transformations of Integer Sequences: Maple, Mathematica, PARI/GP, Sage
- More Transformations of Integer Sequences has 36 transforms grouped into classes

## Common transforms

- Binomial transform
- Euler transform
- Exp transform
- Fourier transform
- Invert transform
- Lambert transform
- Laplace transform
- Legendre transform
- Möbius transform
- Ordinal transform
- Partition transform
- Records transform
- Revert transform
- Stirling transform

## Other transforms

## References

- Barry, Paul (2005). “A Catalan transform and related transformations on integer sequences”.
*Journal of Integer Sequences***8**: pp. Article 05.4.4 . - M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers,
*Linear Algebra and Its Applications***226-228**(1995), pp. 57-72; errata**320**(2000), p. 210. arXiv:math.CO/0205301 - P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102.
- Robert Donaghey, "Binomial self-inverse sequences and tangent coefficients",
*Journal of Combinatorial Theory, Series A*,**21**:2 (1976), pp. 155-163. - Tanya Khovanova, How to Create a New Integer Sequence, arXiv:0712.2244
- Clark Kimberling, "Fractal sequences and interspersions," Ars Combinatoria 45 (1997) 157-168.
- Clark Kimberling, Matrix transformations of integer sequences,
*Journal of Integer Sequences***6**(2003), Article 03.3.3. - Valery A. Liskovets, Some easily derivable integer sequences,
*Journal of Integer Sequences***3**(2000), Article 00.2.2. - Millar, J.; Sloane, N. J. A.; Young, N. E. (1996). “A new operation on sequences: the Boustrophedon transform”.
*J. Comb. Theory***17A**: pp. 44–54 . - Putievskiy, Boris (2012). “Transformations, integer sequences, and pairing functions”.
*arΧiv:1212.2732*. - N. J. A. Sloane and S. Plouffe, The Encyclopedia of Integer Sequences, San Diego, CA, Academic Press, 1995.

## Cite this as

Charles R Greathouse IV, *Sequence transforms*. — From the On-Line Encyclopedia of Integer Sequences® (OEIS®) wiki. (Available at https://oeis.org/wiki/Sequence_transforms)