Coordination Sequences, Planing Numbers, and Other Recent Sequences (II) (Part I)

Neil Sloane, the OEIS Foundation and Rutgers University

Rutgers Experimental Math Seminar, Jan. 31, 2019

Take the graph of a periodic tiling of the plane. 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 simple method for obtaining generating functions for such sequences. There are a number of interesting open questions. I will also discuss Lenormand's "raboter" operation that planes down numbers (e.g., 231 = 11100111_2 becomes 27 = 11011_2). This is an updated version of a talk given to just 4 people during the blizzard of Nov 15 2018. There is also a lovely new open problem: the knight's-move version of the Ulam-Warburton cellular automaton (A319018).