2011/07/19 by Rafal Drabek, Abraham Isgur, Drabek, Rafal +6
Computer Science · Mathematics · #11B37 #Algorithms and Data Compression #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:11B37
paper · pdf · doi:10.48550/arxiv.1107.3852
To appear in "Journal of Difference Equations and Applications"
arxiv created 2011/07/19 · openalex publication_date 2011/07/19 · arxiv updated 2011/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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). Further, given appropriate initial conditions, we derive necessary and sufficient conditions on the parameters s1, a1, s2 and a2 so that C(n) solves the nested recursion R(n) = R(n - s1 - R(n - a1)) + R(n- s2 - R(n - a2)).