The symbolic character of Mathematica makes possible a uniquely coherent approach to integer sequences, integrating functional forms, equations, generating functions, and explicit lists of values. Powerful new algorithms developed at Wolfram Research make possible recognition of functional forms for an extremely wide range of classes of integer sequences.
Table — generate a sequence from a formula
RecurrenceTable — generate a sequence from a recurrence or functional equation
LinearRecurrence — generate a linear recurrence sequence
FindLinearRecurrence — find, if possible, a linear recurrence for a sequence
FindSequenceFunction — find general functional forms for integer sequences
FindGeneratingFunction — find generating functions for integer sequences
DifferenceRoot — general representation of solutions to linear difference equations