Tani, Nesrine Benyahia; Bouroubi, Sadek Enumeration of the partitions of an integer into parts of a specified number of different sizes and especially two sizes. (English) Zbl 1217.05035 J. Integer Seq. 14, No. 3, Article 11.3.6, 12 p. (2011). Summary: 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. Cited in 5 Documents MSC: 05A17 Combinatorial aspects of partitions of integers 11P83 Partitions; congruences and congruential restrictions Keywords:integer partitions; partitions into parts of different sizes; partitions into parts of two sizes; number of divisors Software:OEIS PDFBibTeX XMLCite \textit{N. B. Tani} and \textit{S. Bouroubi}, J. Integer Seq. 14, No. 3, Article 11.3.6, 12 p. (2011; Zbl 1217.05035) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Number of partitions of n with exactly two part sizes. Number of partitions of n into exactly 2 types of odd parts. Number of partitions of n into exactly 2 types of parts: one odd and one even. Triangular array read by rows: T(n,k) is the number of partitions of n into k parts of 2 different sizes; n>=3, 2<=k<=n-1.