Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.4

Partitions Excluding Specific Polygonal Numbers As Parts

James A. Sellers
Department of Mathematics
The Pennsylvania State University
University Park, PA 16802
USA

Abstract: Many results appear in the literature involving partitions of an integer n into parts which are certain polygonal numbers (such as triangular numbers or squares). However, few results appear which deal with partition functions that exclude specific polygonal numbers as parts. We consider such functions in this note, and prove two families of partition identities.

(Concerned with sequences A000217 A000290 A001156 A002635 A002636 A007294 A087153 .)

Received September 13 2003; revised version received May 10 2004. Published in Journal of Integer Sequences June 8 2004.