14 citations · 49 across the 7 of their papers we have counts for
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Nested Recurrence Relations With Conolly-Like Solutions
Alejandro Erickson, Abraham Isgur, Bradley W. Jackson +2
A nondecreasing sequence of positive integers is -Conolly, or Conolly-like for short, if for every positive integer the number of times that occurs in the sequence i…
Nested Recursions, Simultaneous Parameters and Tree Superpositions
Abraham Isgur, Vitaly Kuznetsov, Mustazee Rahman +1
We apply a tree-based methodology to solve new, very broadly defined families of nested recursions of the general form R(n)=sum_{i=1}^k R(n-a_i-sum_{j=1}^p R(n-b_{ij})), where a_i…
Nested recursions with ceiling function solutions
Abraham Isgur, Vitaly Kuznetsov, Stephen M. Tanny
Consider a nested, non-homogeneous recursion R(n) defined by R(n) = \sum_{i=1}^k R(n-s_i-\sum_{j=1}^{p_i} R(n-a_ij)) + nu, with c initial conditions R(1) = xi_1 > 0,R(2)=xi_2 > 0,…
A combinatorial approach for solving certain nested recursions with non-slow solutions
Abraham Isgur, Vitaly Kuznetsov, Stephen Tanny
We define the generalized Golomb triangular recursion by g_{j,s,lambda}(n) = g_{j,s,lambda}(n - s - g_{j,s,lambda}(n-j)) + λj. For particular choices of the initial conditions, we…
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…