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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/129168
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- Title
- On the g-ary expansions of Apéry, Motzkin, Schröder and other combinatorial numbers
- Related
- Annals of combinatorics, Vol. 14, No. 4, (2010), p.507-524
- DOI
- 10.1007/s00026-011-0074-9
- Publisher
- Birkhäuser
- Date
- 2010
- Author/Creator
- Luca, Florian
- Author/Creator
- Shparlinski, Igor E
- Description
- 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 = h1(n)u n+1 + h2(n)u n with two nonconstant rational functions h1(X), h2(X)ϵ Q [X]. This class includes the Apéry, Delannoy, Motzkin, and Schröder numbers.
- Description
- 18 page(s)
- Subject Keyword
- 010100 Pure Mathematics
- Subject Keyword
- Apéry numbers
- Subject Keyword
- Motzkin numbers
- Subject Keyword
- Schröder numbers
- Subject Keyword
- representations in integer bases of special numbers
- Subject Keyword
- applications to S-unit equations
- Resource Type
- journal article
- Organisation
- Macquarie University. Department of Computing
- Identifier
- http://hdl.handle.net/1959.14/129168
- Identifier
- mq:13986
- Identifier
- ISSN:0218-0006
- Identifier
- mq-rm-2010006012
- Language
- eng
- Reviewed
