FindSequenceFunction [{a1,a2,a3,…}]
attempts to find a simple function that yields the sequence an when given successive integer arguments.
FindSequenceFunction [{{n1,a1},{n2,a2},…}]
attempts to find a simple function that yields ai when given argument ni.
FindSequenceFunction [n1a1,n2a2,…]
gives a function that yields ai when given argument ni.
FindSequenceFunction [{n1a1,n2a2,…}]
gives a function that yields ai when given argument ni.
FindSequenceFunction [list,n]
gives the function applied to n.
FindSequenceFunction
FindSequenceFunction [{a1,a2,a3,…}]
attempts to find a simple function that yields the sequence an when given successive integer arguments.
FindSequenceFunction [{{n1,a1},{n2,a2},…}]
attempts to find a simple function that yields ai when given argument ni.
FindSequenceFunction [n1a1,n2a2,…]
gives a function that yields ai when given argument ni.
FindSequenceFunction [{n1a1,n2a2,…}]
gives a function that yields ai when given argument ni.
FindSequenceFunction [list,n]
gives the function applied to n.
Details and Options
- The sequence elements an can be either exact numbers or symbolic expressions.
- FindSequenceFunction finds results in terms of a wide range of integer functions, as well as implicit solutions to difference equations represented by DifferenceRoot .
- If FindSequenceFunction cannot find a simple function that yields the specified sequence, it returns unevaluated.
- The following options can be used:
-
TimeConstraint 10 how many seconds to search a particular function space or perform a transformation
- FindSequenceFunction [list] by default uses earlier elements in list to find candidate simple functions, then validates the functions by looking at later elements.
- FindSequenceFunction [list] only returns functions that correctly reproduce all elements of list.
Examples
open all close allBasic Examples (2)
Find a sequence that yields the sequence 1,1,2,3,5,8,13,…:
Find a function that yields the given sequence as a subsequence:
Check the even subsequence:
Scope (5)
Periodic sequences:
Polynomial functions:
Rational functions:
Hypergeometric terms:
Recurrence equations:
Generalizations & Extensions (1)
FindSequenceFunction works on arbitrary exact numbers or symbolic expressions:
Applications (6)
Find formulas for complex sequences:
Use additional values to validate the result:
Find a closed form for a sequence of definite integrals:
Find a closed form for the number of 0,1 sequences of length containing two adjacent 1s:
Generate a sequence from a power series expansion:
Find its formula:
Use SeriesCoefficient to find an alternative formula:
FindSequenceFunction assumes that sequences start with index 1:
Compare the result:
Compute a finite number of Fourier coefficients:
Find the formula:
Use a FourierCoefficient directly:
Verify the consistency of formulas:
Construct the Cantor set by starting with a {0,1} interval and removing the middle third of each interval in each step:
Some steps:
Find the length of the region:
Find a formula for the sequence of lengths using FindSequenceFunction :
Properties & Relations (2)
Sum , Product , and other general discrete functions may be used:
Find the generating function of a sequence:
Use FindGeneratingFunction :
Related Links
Text
Wolfram Research (2008), FindSequenceFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/FindSequenceFunction.html (updated 2015).
CMS
Wolfram Language. 2008. "FindSequenceFunction." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/FindSequenceFunction.html.
APA
Wolfram Language. (2008). FindSequenceFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindSequenceFunction.html
BibTeX
@misc{reference.wolfram_2025_findsequencefunction, author="Wolfram Research", title="{FindSequenceFunction}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindSequenceFunction.html}", note=[Accessed: 24-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_findsequencefunction, organization={Wolfram Research}, title={FindSequenceFunction}, year={2015}, url={https://reference.wolfram.com/language/ref/FindSequenceFunction.html}, note=[Accessed: 24-November-2025]}