Integer Partition/Table
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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 $n$.
- $\begin{array} {|r|r|} \hline n & \map p n \\ \hline 1 & 1 \\ 2 & 2 \\ 3 & 3 \\ 4 & 5 \\ 5 & 7 \\ 6 & 11 \\ 7 & 15 \\ 8 & 22 \\ 9 & 30 \\ 10 & 42 \\ 11 & 56 \\ 12 & 77 \\ 13 & 101 \\ 14 & 135 \\ 15 & 176 \\ 16 & 231 \\ 17 & 297 \\ 18 & 385 \\ 19 & 490 \\ 20 & 627 \\ 21 & 792 \\ 22 & 1002 \\ 23 & 1255 \\ 24 & 1575 \\ 25 & 1958 \\ 26 & 2436 \\ 27 & 3010 \\ 28 & 3718 \\ 29 & 4565 \\ 30 & 5604 \\ \hline \end{array}$
This sequence is A000041 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-5}$ The Use of Computers in Number Theory: Exercise $8$
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.1$: Mathematical Induction