Integer Partition/Examples

Examples of Integer Partitions

Partitions of $4$

The integer $4$ can be partitioned as follows:

$4$

$3 + 1$

$2 + 2$

$2 + 1 + 1$

$1 + 1 + 1 + 1$

Partitions of $5$

The integer $5$ can be partitioned as follows:

$5$

$4 + 1$

$3 + 2$

$3 + 1 + 1$

$2 + 2 + 1$

$2 + 1 + 1 + 1$

$1 + 1 + 1 + 1 + 1$

The sequence grows rapidly: $\map p {200} = 3 \, 972 \, 999 \, 029 \, 288$ for example.

Table of Integer Partitions

The following table presents a list of the number of integer partitions for all $n$ from $1$ to $30$.

In the following, $\map p n$ denotes the number of integer partitions for $n$.

$\begin{array} {|r|r|}

\hline n & \map p n \\ \hline 1 & 1 \\ 2 & 2 \\ 3 & 3 \\ 4 & 5 \\ 5 & 7 \\ 6 & 11 \\ 7 & 15 \\ 8 & 22 \\ 9 & 30 \\ 10 & 42 \\ 11 & 56 \\ 12 & 77 \\ 13 & 101 \\ 14 & 135 \\ 15 & 176 \\ 16 & 231 \\ 17 & 297 \\ 18 & 385 \\ 19 & 490 \\ 20 & 627 \\ 21 & 792 \\ 22 & 1002 \\ 23 & 1255 \\ 24 & 1575 \\ 25 & 1958 \\ 26 & 2436 \\ 27 & 3010 \\ 28 & 3718 \\ 29 & 4565 \\ 30 & 5604 \\ \hline \end{array}$