Constant-recursive sequence

In mathematics, a constant-recursive sequence or C-finite sequence is a sequence satisfying a linear recurrence with constant coefficients.

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

where the d coefficients ${\displaystyle c_{1},c_{2},\dots ,c_{d}}$ are constants.

A sequence ${\displaystyle s(0),s(1),s(2),\dots }$ is a constant-recursive sequence if there is an order-d homogeneous linear recurrence with constant coefficients that it satisfies for all ${\displaystyle n\geq d}$.

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