Partition of Integer where Part Appears no more than Twice/Examples

Examples of Partition of Integer where Part Appears no more than Twice

Partition of $4$ where Part Appears no more than Twice

The integer $4$ can be partitioned such that no part appears more than twice as follows:

$4$

$3 + 1$

$2 + 2$

$2 + 1 + 1$

Table of Partitions of Integers where Part Appears no more than Twice

The following table presents a list of the number of ways a positive integer $n$ can be partitioned such that no part appears more than twice for all $n$ from $1$ to $15$.

In the following, $\map v n$ denotes the number of such partitions for $n$.

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

\hline n & \map v n \\ \hline 1 & 1 \\ 2 & 2 \\ 3 & 2 \\ 4 & 4 \\ 5 & 5 \\ 6 & 6 \\ 7 & 9 \\ 8 & 13 \\ 9 & 16 \\ 10 & 22 \\ 11 & 27 \\ 12 & 36 \\ 13 & 44 \\ 14 & 57 \\ 15 & 70 \\ \hline \end{array}$