International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 387-396

Lucas partitions

Neville Robbins

Mathematics Department, San Francisco State University, San Francisco 94132, CA, USA

Received 1 April 1996

Copyright © 1998 Neville Robbins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Lucas sequence is defined by: L0=2,L1=1,Ln=Ln1+Ln2 for n2. Let V(n), r(n) denote respectively the number of partitions of n into parts, distinct parts from {Ln}. We develop formulas that facilitate the computation of V(n) and r(n).