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

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.

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.