Partition of Integer into Parts not Multiple of 3/Examples

Examples of Partition of Integer into Parts not Multiple of 3

Partition of $4$ into Parts not Multiple of $3$

The integer $4$ can be partitioned into parts which are specifically not multiples of $3$ as follows:

$4$

$2 + 2$

$2 + 1 + 1$

$1 + 1 + 1 + 1$

Table of Partitions of Integers into Parts not Multiple of $3$

The following table presents a list of the number of ways a positive integer $n$ can be partitioned into parts which are specifically not multiples of $3$ for all $n$ from $1$ to $15$.

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

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

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