  We introduce a family of extensions of the Hietarinta-Viallet equation to a
multi-term recurrence relation via a reduction from the coprimeness-preserving
extension to the discrete KdV equation. The recurrence satisfies the
irreducibility and the coprimeness property although it is nonintegrable in
terms of an exponential degree growth. We derive the algebraic entropy of the
recurrence by an elementary method of calculating the degree growth. The result
includes the entropy of the original Hietarinta-Viallet equation.
