2
$\begingroup$

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.

  1. each of its terms is an element of the set of consecutive integers $\{1,2,3,4,\ldots ,N\}$,
  2. the sequence is increasing, and
  3. 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!

3 Answers 3