Let c(n) be the number of ways of writing n as a sum, where order matters.
So we have: .3 = 3, 3 = 1 + 2, 3 = 2 + 1, 3 = 1 + 1 + 1
Thus: c(3) = 4.
I don't understand that equation.
Both sums diverge to infinity.
We have a board which is units long.
. . . . .
There are places where the board can be cut.
For each place, there are two choices: cut or not cut.