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
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 
@article{JIS_2011__14_3_a5,
     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},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {3},
     zbl = {1217.05035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a5/}
}
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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/