Abstract
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. We investigate the set of sequences which satisfy linear recurrence equations with coefficients that are C-finite sequences. These sequences are a natural generalization of holonomic sequences. In this paper, we show that C2-finite sequences form a difference ring and provide methods to compute in this ring.
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