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# Recurrence relations with constant coefficients

A **recurrence relation with constant coefficients** of degree is an equation of the form

## Contents

- 1 Linear recurrence relations with constant coefficients
- 2 Quadratic recurrence relations with constant coefficients

## Linear recurrence relations with constant coefficients

Cf. Index entries for sequences related to linear recurrences with constant coefficients.

### Homogeneous linear recurrence relations with constant coefficients

An order homogeneous linear recurrence relation with constant coefficients is an equation of the form

where the coefficients are constants.

### Nonhomogeneous linear recurrence relations with constant coefficients

An order nonhomogeneous linear recurrence relation with constant coefficients is an equation of the form

where and the coefficients are constants.

## Quadratic recurrence relations with constant coefficients

### Homogeneous quadratic recurrence relations with constant coefficients

(...)

### Nonhomogeneous quadratic recurrence relations with constant coefficients

(...)

### Bilinear recurrence relations with constant coefficients

#### Homogeneous bilinear recurrence relations with constant coefficients

A homogeneous bilinear recurrence relation with constant coefficients is an equation of the form

where the coefficients are constants. (Note that there are no squared .)

#### Nonhomogeneous bilinear recurrence relations with constant coefficients

A nonhomogeneous bilinear recurrence relation with constant coefficients is an equation of the form

where either or and the coefficients and and are constants. (Note that there are no squared .)