BUILT-IN WOLFRAM LANGUAGE 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 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.
Introduced in 2008
(7.0)