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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[list, n]
gives the function applied to n.
  • The sequence elements an can be either exact numbers or symbolic expressions.
  • If FindSequenceFunction cannot find a simple function that yields the specified sequence, it returns unevaluated.
  • The following options can be used:
FunctionSpaceAutomaticwhere to look for candidate simple functions
MethodAutomaticmethod to use
TimeConstraint10how many seconds to search a particular function space or perform a transformation
ValidationLengthAutomaticsequence length used to validate a candidate function found
  • FindSequenceFunction[list] by default uses earlier elements in list to find candidate simple functions, then validates the functions by looking at later elements.
EXAMPLESCLOSE ALL
Basic 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:
Find a sequence that yields the sequence 1, 1, 2, 3, 5, 8, 13, ...:
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Find a function that yields the given sequence as a subsequence:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
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Out[2]=
Check the even subsequence:
In[3]:=
Click for copyable input
Out[3]=
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   (5)
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 n 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:
Properties & Relations   (2)
Sum, Product and other general discrete functions may be used:
Find the generating function of a sequence:
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