### Related

##### num_partitions

num_partitions (30);

Calculate

##### num_partitions

num_partitions(12);

Calculate

##### num_partitions

? num_partitions;

Calculate

##### num_partitions

num_partitions (30);

Calculate

##### num_partitions

num_partitions(12);

Calculate

##### num_partitions

? num_partitions;

Calculate

### num_partitions

Run Example
```(%i1)num_partitions (5) = cardinality (integer_partitions (5));
(%o1)                                7 = 7
(%i2)  num_partitions (8, list);
(%o2)                   [1, 1, 2, 3, 5, 7, 11, 15, 22]
(%i3)  num_partitions (n);
(%o3)                          num_partitions(n)
(%i4) ```
Run Example
```num_partitions (5) = cardinality (integer_partitions (5));
(%o1)                                7 = 7
(%i2)  num_partitions (8, list);
(%o2)                   [1, 1, 2, 3, 5, 7, 11, 15, 22]
(%i3)  num_partitions (6);
(%o3)                                 11
(%i4) ```
Run Example
```? num_partitions;

-- Function: num_partitions (<n>)
-- Function: num_partitions (<n>, list)
Returns the number of integer partitions of <n> when <n> is a
nonnegative integer.  Otherwise, `num_partitions' returns a noun
expression.

`num_partitions(<n>, list)' returns a list of the number of
integer partitions of 1, 2, 3, ..., <n>.

For a nonnegative integer <n>, `num_partitions(<n>)' is equal to
`cardinality(integer_partitions(<n>))'; however, `num_partitions'
does not actually construct the set of partitions, so it is much
faster.

Examples:

(%i1) num_partitions (5) = cardinality (integer_partitions (5));
(%o1)                         7 = 7
(%i2) num_partitions (8, list);
(%o2)            [1, 1, 2, 3, 5, 7, 11, 15, 22]
(%i3) num_partitions (n);
(%o3)                   num_partitions(n)

(%o1)                                true
(%i2) ```

### Related Help

Help for Num_partitions