Partitions With No Ones

A partition of is an expression of as a sum of not necessarily distinct positive integers, where the order does not matter. Note that \(n = n\) counts as a partition of \(n\).

Let \(C'_n\) the number of partitions of \(n\) with no part equal to 1.

For instance, \(C'_8 = 7\) because \[8 = 8 = 6 + 2 = 5 + 3 = 4 + 4 \\ = 4 + 2 + 2 = 3 + 3 + 2 = 2 + 2 + 2 + 2.\] Find \(C'_{50}\).


Inspired by Patrick Corn.

×

Problem Loading...

Note Loading...

Set Loading...