# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# 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 OptionsDetails 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:
•  FunctionSpace Automatic where to look for candidate simple functions Method Automatic method to use TimeConstraint 10 how many seconds to search a particular function space or perform a transformation ValidationLength Automatic sequence 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.
• FindSequenceFunction[list] only returns functions that correctly reproduce all elements of list.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Find a sequence that yields the sequence 1,1,2,3,5,8,13,:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=

Find a function that yields the given sequence as a subsequence:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=

Check the even subsequence:

 In[3]:=
 Out[3]=