Nested recursions, simultaneous parameters and linear combinations of trees

在我的研究中，我专注于开发解决嵌套(也称为自引用或元斐波那契)递归的方法。不严格地说，这些是递归，其中递归中的一个或多个参数依赖于解决方案的较早项。最早的嵌套递归出现在大约40年前，包括所谓的‘Golomb’递归a(N)=a(n-a(n-1))+1、Hofstadter q-递归q(n-q(n-1))+q(n-q(n-2))和Conolly递归C(n-C(n-1))+C(n-1-C(n-2))。

In my research I focus on developing methodologies to solve nested (also called self-referencing or meta-Fibonacci) recursions. Loosely speaking, these are recursions in which one or more of the arguments in the recursion depend upon earlier terms of the solution. The earliest examples of nested recursions appeared about forty years ago, and include the so-called ``Golomb" recursion a(n) = a(n-a(n-1)) + 1, the Hofstadter Q-recursion Q(n) = Q(n-Q(n-1)) + Q(n-Q(n-2)) and the Conolly recursion C(n) = C(n-C(n-1))+C(n-1-C(n-2)).