A sequence is called C-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with C-finite coefficients. Recently, it was shown that such C2-finite sequences satisfy similar closure properties as C-finite sequences. In particular, they form a difference ring.

A sequence is called C-finite, if it satisfies a linear recurrence with constant coefficients and holonomic, if it satisfies a linear recurrence with polynomial coefficients. The class of C2-finite sequences is a natural generalization of holonomic sequences and consists of sequences satisfying a linear recurrence with C-finite coefficients whose leading coefficient has no zero terms. Recently, we investigated computational properties of $C^2$-finite sequences: we showed that these sequences form a difference ring and provided methods to compute in this ring.

Holonomic sequences are widely studied as many objects interesting to mathematicians and computer scientists are in this class. In the univariate case, these are the sequences satisfying linear recurrences with polynomial coefficients and also referred to as D-finite sequences. A subclass are C-finite sequences satisfying a linear recurrence with constant coefficients.