### Abstract

Let g ≥ 2 be an integer and let (u_{n})_{n≥1} be a sequence of integers which satisfies a relation u_{n+1} = h(n)u_{n} for a rational function h(X). For example, various combinatorial numbers as well as their products satisfy relations of this type. Here, we show that under some mild technical assumptions the number of nonzero digits of u_{n} in base g is large on a set of n of asymptotic density 1. We also extend this result to a class of sequences satisfying relations of second order u_{n+2} = h_{1}(n)u_{n+1} + h_{2}(n)u_{n} with two nonconstant rational functions h_{2}(X),h_{2}(X) ∈ Q[X]. This class includes the Apéry, Delannoy, Motzkin, and Schröder numbers.

Original language | English |
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Pages (from-to) | 507-524 |

Number of pages | 18 |

Journal | Annals of Combinatorics |

Volume | 14 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2010 |