A combinatorial approach for solving certain nested recursions with non-slow solutions
نویسندگان
چکیده
منابع مشابه
Nested Recursions with Ceiling Function Solutions
Unless otherwise noted, we consider only n > 0. The parameters in (1.1) are all integers satisfying k, pi and aij > 0. Assume c initial conditions R(1) = ξ1, R(2) = ξ2, . . . , R(c) = ξc, with all ξi > 0. Golomb [6] first solved the simplest example of such a non-homogeneous nested recursion, namely, G(n) = G(n− G(n− 1)) + 1, G(1) = 1; see also [7]. In fact, all of the recursions we find with c...
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15 صفحه اولSums of Ceiling Functions Solve Nested Recursions
It is known that, for given integers s ≥ 0 and j > 0, the nested recursion R(n) = R(n−s−R(n− j))+R(n−2j−s−R(n−3j)) has a closed form solution for which a combinatorial interpretation exists in terms of an infinite, labeled tree. For s = 0, we show that this solution sequence has a closed form as the sum of ceiling functions C(n) = ∑j−1 i=0 ⌈
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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2013
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236198.2012.662967