With IntegerPartitions[7]
, I have partitions of 7 into integers that are smaller than 6 as follows.
{5, 2},
{5, 1, 1},
{4, 3},
{4, 2, 1},
{4, 1, 1, 1},
{3, 3, 1},
{3, 2, 2},
{3, 2, 1, 1},
{3, 1, 1, 1, 1},
{2, 2, 2, 1},
{2, 2, 1, 1, 1},
{2, 1, 1, 1, 1, 1},
{1, 1, 1, 1, 1, 1, 1}
Furthermore, I want to include the permutation of each partition. For the first partition, for example, I also want to include {2, 5}
.
Question
How to calculate the whole permutation of the partition of 7 given above? I don't need the list for sure, but just the length of the list.