BUILT-IN WOLFRAM LANGUAGE SYMBOL

FindSequenceFunction

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

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

FindSequenceFunction[n₁a₁,n₂a₂,…]
gives a function that yields a_i when given argument n_i.

FindSequenceFunction[{n₁a₁,n₂a₂,…}]
gives a function that yields a_i when given argument n_i.

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

Details and Options Details and Options

The sequence elements a_n 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.