Examples for


Recurrences, or recurrence relations, are equations that define sequences of values using recursion and initial values. Recurrences can be linear or non-linear, homogeneous or non-homogeneous, and first order or higher order. Wolfram|Alpha has the power to solve various kinds of recurrences and to find recurrence relations satisfied by given sequences.

Solving Recurrences

Find closed-form solutions for recurrence relations and difference equations.

Solve a recurrence:

Specify initial values:

Solve a q -difference equation:

More examples

Finding Recurrences

Deduce recurrence relations to model sequences of numbers or functions.

Find a recurrence satisfied by a given sequence:

Find a recurrence satisfied by a sequence of functions:

More examples