### The Maxima on-line user's manual

Algebra Calculator

#### Num_distinct_partitions

Function: num_distinct_partitions (<n>)

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

`num_distinct_partitions(<n>, list)` returns a list of the number of distinct partitions of 1, 2, 3, ..., <n>.

A distinct partition of <n> is a list of distinct positive integers k_1, ..., k_m such that <n> = k_1 + ... + k_m.

Examples:

```          (%i1) num_distinct_partitions (12);
(%o1)                          15
(%i2) num_distinct_partitions (12, list);
(%o2)      [1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15]
(%i3) num_distinct_partitions (n);
(%o3)              num_distinct_partitions(n)```

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

### Related Examples

##### num_distinct_partitions

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##### num_distinct_partitions

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