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PARTP (n,k)


  • and are any integers.
    • PARTP() shows the number of partitions of a given number.



  • is any integer. is the number of ways.
  • A partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.
  • Two sums that differ only in the order of their summands are considered the same partition.
  • By convention, partitions are usually ordered from largest to smallest.
  • Partition of a number is also called the number of unrestricted partition.
  • When explicitly listing the partitions of a number n, the simplest form is the so-called natural representation which simply gives the sequence of numbers in the representation.
  • The multiplicity representation instead gives the number of times each number occurs together with that number.


  1. PARTP(10,3) = 8
  2. PARTP(54,10) = 29292

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