Neil Sloane, OEIS Foundation

Abstract

Take a periodic tiling of the plane and consider its associated graph. The coordination sequence with respect to a node P gives the number of nodes that are n edges away from P. Chaim Goodman-Strauss and I have a new and simple method for obtaining generating functions for such sequences, which will be illustrated with several examples. There are a number of interesting open questions. I will also discuss Lenormand's operation that planes down numbers (e.g., 231 becomes 27).