Where does 13 come from?

Question

I am going over the Rod Cutting Problem

Everything makes sense to me until

For example, $L$ = {9} has the total cost Cost($L$) = $P$[9] = 13,
whereas $L$' = {1,1,1,1,1,1,1,1,1} has the total cost Cost(L') = 9*P[1] = 9 $\lt$ 13

Earlier the author states "Selling a rod of length $i$ units earns $P$[i] dollars." Here is the table $P$ for this problem

Shouldn't the first cost be 22, if you look at the table? (P[9] = 22) Does anyone know where the 13 is coming from?

One thought I had was that the 13 is the dollars earned minus the length, 22 - 9 which doesn't make sense in the situation either. But this wouldn't work because in the second example, the author doesn't subtract the dollars earned, 9, by the length, 1.

Answer 1

Looks like a typo to me!

There's another typo in the definition of the problem. I think it should read $$\text{Cost}(L) = \sum_{j = 1}^k P[l_j] = \dots$$ instead of $$\text{Cost}(L) - \sum_{j = 1}^k P[l_j] = \dots$$