Abstract
Let F-i denote the ith Fibonacci number, and define Pi(n)(i=1) (1+ chi(Fi+1)) = Sigma(k) c(n)(k)chi(k). The paper is concerned primarily with the coefficients c(n)(k). In particular, for any r >= 0 the generating function Sigma(n >= 0)(Sigma(k) c(n)(k)(r))chi(n) is rational. The coefficients c(n)(k) can be displayed in an array called the Fibonacci triangle poset F with some interesting further properties, including an encoding of a certain dense linear order on the nonnegative integers. Some generalizations are briefly considered, but there remain many open questions. (c) 2023 Elsevier Ltd. All rights reserved.