14 citations · 25 across the 3 of their papers we have counts for
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Sums of Ceiling Functions Solve Nested Recursions
Rafal Drabek, Abraham Isgur, Vitaly Kuznetsov +1
It is known that, for given integers s \geq 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 combinat…
Spot-Based Generations for Meta-Fibonacci Sequences
Barnaby Dalton, Mustazee Rahman, Stephen Tanny
For many meta-Fibonacci sequences it is possible to identify a partition of the sequence into successive intervals (sometimes called blocks) with the property that the sequence beh…
A Combinatorial Interpretation for Certain Relatives of the Conolly Sequence
B. Balamohan, Zhiqiang Li, Stephen Tanny
For any integer s >= 0, we derive a combinatorial interpretation for the family of sequences generated by the recursion (parameterized by s) h_s(n) = h_s(n - s - h_s(n - 1)) + h_s(…