12 citations · 16 across the 3 of their papers we have counts for
7 papers
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…
On variants of Conway and Conolly's Meta-Fibonacci recursions
Abraham Isgur, Mustazee Rahman
We study the recursions where , are integers and the superscript denotes a -fold composition, and also the recurs…
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…