An extension of holonomic sequences: C2-finite sequences

Holonomic sequences are widely studied as many objects interesting to mathematicians and computer scientists in this class. In the univariate case, these satisfying linear recurrences with polynomial coefficients also referred D-finite sequences. A subclass C-finite a recurrence constant coefficients. We investigate set of which satisfy equations that call them C2-finite These natural generalization holonomic paper, we show form difference ring provide methods compute ring. Furthermore, an analogous construction for D2-finite sequences, i.e., constructions can be iterated obtain increasing chain rings.