Geodesic
Enumeration of the partitions of an integer into parts of a specified number of different sizes and especially two sizes
Journal of integer sequences, Tome 14 (2011) no. 3.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 05A17, 11P83
Keywords: integer partitions, partitions into parts of different sizes, partitions into parts of two sizes, number of divisors 
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     author = {Tani, Nesrine Benyahia and Bouroubi, Sadek},
     title = {Enumeration of the partitions of an integer into parts of a specified number of different sizes and especially two sizes},
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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. Journal of integer sequences, Tome 14 (2011) no. 3. http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a5/