I need help primarily with the finding a solution, I already came up with an answer.
We define an Eden sequence to be a subset of the set $\{1,2,3,4,\ldots ,N\}$. The Eden sequence has three conditions.
- each of its terms is an element of the set of consecutive integers $\{1,2,3,4,\ldots ,N\}$,
- the sequence is increasing, and
- the terms in odd numbered positions are odd and the terms in even numbered positions are even.
We then define a function $e(N)$ such that $e(N)$ denotes the number of Eden sequences of the set $\{1,2,3,4,\ldots ,N\}$. If we are given that $e(17)=4180$ and $q(20)=17710$, how would we find $e(18)$ and $e(19)$ using a mathematical approach?
I am pretty sure the answers are that $e(18) = 6764$ and $e(19) = 10945$.
Thanks for your help in advance!