Journal of Integer Sequences, Vol. 14 (2011), Article 11.3.6

Enumeration of the Partitions of an Integer into Parts of a Specified Number of Different Sizes and Especially Two Sizes

Nesrine Benyahia Tani
Algiers 3 University
Faculty of Economics and Management Sciences
2 Ahmed Waked Street
Dely Brahim, Algiers

Sadek Bouroubi
University of Science and Technology Houari Boumediene
Faculty of Mathematics
P. O. Box 32
16111 El-Alia, Bab-Ezzouar, Algiers


A partition of a non-negative integer n is a way of writing n as a sum of a nondecreasing sequence of parts. The present paper provides the number of partitions of an integer n into parts of a specified number of different sizes. We establish new formulas for such partitions with particular interest to the number of partitions of $n$ into parts of two sizes. A geometric application is given at the end of this paper.

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(Concerned with sequences A002133 A117955 A117956.)

Received May 4 2010; revised version received October 3 2010; January 31 2011; February 28 2011. Published in Journal of Integer Sequences, March 25 2011.

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