BUILT-IN MATHEMATICA SYMBOL

# FindSequenceFunction

FindSequenceFunction[{a1, a2, a3, ...}]
attempts to find a simple function that yields the sequence when given successive integer arguments.

FindSequenceFunction[{{n1, a1}, {n2, a2}, ...}]
attempts to find a simple function that yields when given argument .

FindSequenceFunction[list, n]
gives the function applied to n.

## Details and OptionsDetails and Options

• The sequence elements 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,...:

 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]=