Broadcast, Reduction and Scan are popular functional skeletons which are used in distributed algorithms to distribute and gather data. We derive new parallel implementations of combinations of Broadcast, Reduction and Scan via a tabular classification of linearly recursive functions. The trick in the derivation is to not simply combine the individual parallel implementations of Broadcast, Reduction and Scan, but to transform these combinations to skeletons with a better performance. These skeletons are also linearly recursive. Keywords: functional programming, linear recursion, parallelization, skeletons 1. Introduction Functional programming offers a very high-level approach to specifying executable problem solutions. For example, the scheme of linear recursion can be expressed concisely as a higher-order function. In the data-parallel world, higher-order functions are used which represent classes of parallel algorithms on data structures; these higher-order functions are also call...