# 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:
•  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.

# Examples

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## 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]=

## Properties & Relations(2)

Introduced in 2008
(7.0)
| Updated in 2015
(10.1)