Partition of Integer into Powers of 2/Table

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Table of Partition of Integer into Powers of 2

The following table presents a list of the number of ways a positive integer $n$ can be partitioned into (integer) powers of $2$ for all $n$ from $1$ to $40$.

In the following, $\map b n$ denotes the number of integer partitions into (integer) powers of $2$ for $n$.


$\begin{array} {|r|r|} \hline n & \map b n \\ \hline 1 & 1 \\ 2 & 2 \\ 3 & 2 \\ 4 & 4 \\ 5 & 4 \\ 6 & 6 \\ 7 & 6 \\ 8 & 10 \\ 9 & 10 \\ 10 & 14 \\ 11 & 14 \\ 12 & 20 \\ 13 & 20 \\ 14 & 26 \\ 15 & 26 \\ 16 & 36 \\ 17 & 36 \\ 18 & 46 \\ 19 & 46 \\ 20 & 60 \\ \hline \end{array} \qquad \begin{array} {|r|r|} \hline n & \map b n \\ \hline 21 & 60 \\ 22 & 74 \\ 23 & 74 \\ 24 & 94 \\ 25 & 94 \\ 26 & 114 \\ 27 & 114 \\ 28 & 140 \\ 29 & 140 \\ 30 & 166 \\ 31 & 166 \\ 32 & 202 \\ 33 & 202 \\ 34 & 238 \\ 35 & 238 \\ 36 & 284 \\ 37 & 284 \\ 38 & 330 \\ 39 & 330 \\ 40 & 390 \\ \hline \end{array}$

This sequence is A018819 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


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