# Manuals/calci/PARTP

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**PARTP (n,k)**

where

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

## Description

PARTP(n,k)

- 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.

## Examples

- PARTP(10,3) = 8
- PARTP(54,10) = 29292

## Related Videos

## See Also

## References