14 citations · 49 across the 7 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…
Solving Non-homogeneous Nested Recursions Using Trees
Abraham Isgur, Mustazee Rahman, Stephen Tanny
The solutions to certain nested recursions, such as Conolly's C(n) = C(n-C(n-1))+C(n-1-C(n-2)), with initial conditions C(1)=1, C(2)=2, have a well-established combinatorial interp…
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…