The symbolic character of the Wolfram Language 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.

Sequence Generation

Table — generate a sequence from a formula

RecurrenceTable — generate a sequence from a recurrence or functional equation

LinearRecurrence — generate a linear recurrence sequence

ShiftRegisterSequence — generate a linear or nonlinear shift-register sequence

Sequence Recognition

FindLinearRecurrence — find, if possible, a linear recurrence for a sequence

FindSequenceFunction — find general functional forms for integer sequences

FindRepeat — find a repeating block in a sequence

FindTransientRepeat — find transient and repeating part of a sequence

Generating Functions

GeneratingFunction  ▪  ExponentialGeneratingFunction

FindGeneratingFunction — find generating functions for integer sequences

Fibonacci, LucasL — Fibonacci and Lucas numbers and polynomials

BernoulliB  ▪  Factorial  ▪  Binomial  ▪  BellB  ▪  CatalanNumber

DifferenceRoot — general representation of solutions to linear difference equations