This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# FindSequenceFunction

 FindSequenceFunction attempts to find a simple function that yields the sequence when given successive integer arguments. FindSequenceFunctionattempts to find a simple function that yields when given argument . FindSequenceFunctiongives the function applied to n.
• The sequence elements 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:
 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.
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,...:
 Out[1]=
 Out[2]=

Find a function that yields the given sequence as a subsequence:
 Out[1]=
 Out[2]=
Check the even subsequence:
 Out[3]=
 Scope   (5)
Periodic sequences:
Polynomial functions:
Rational functions:
Hypergeometric terms:
Recurrence equations:
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 containing two adjacent 1s:
Generate a sequence from a power series expansion:
Find its formula:
Use SeriesCoefficient to find an alternative formula: