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Yossi Moshe 《Journal of Number Theory》2003,103(1):109-121
Let be a double sequence over a finite field satisfying a linear recurrence with constant coefficients, with at most finitely many nonzero elements on each row. Given a nonzero element g of , we show how to obtain an explicit formula for the number of g's in the first qn rows of A. We also characterize the cases when the density of 0's is 1. 相似文献
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Pantelimon St?nic? 《Journal of Number Theory》2003,100(2):203-216
In this paper, we consider the generalized Catalan numbers , which we call s-Catalan numbers. For p prime, we find all positive integers n such that pq divides F(pq,n), and also determine all distinct residues of , q?1. As a byproduct we settle a question of Hough and the late Simion on the divisibility of the 4-Catalan numbers by 4. In the second part of the paper we prove that if pq?99999, then is not squarefree for n?τ1(pq) sufficiently large (τ1(pq) computable). Moreover, using the results of the first part, we find n<τ1(pq) (in base p), for which may be squarefree. As consequences, we obtain that is squarefree only for n=1,3,45, and is squarefree only for n=1,4,10. 相似文献
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