I have a follow-up question here from my previous question on Math SE. I am lazy enough to explain the content again, so I have used a paraphraser to explain it below:
I was considering arbitrary series, springing up as a top priority, when I considered one potential series in my mind. It is as per the following:
The essential thought is, take a line of regular numbers \$\mathbb{N}\$ which goes till boundlessness, and add them. Something apparent here is that the most greatest biggest number \$\mathbb{N}_{max}\$ would be \$\mathbb{N}_{i}\$. In essential words, on the off chance that we go till number 5, \$\mathbb{N}_5\$ the level it comes to by summation is 5.
Further, continuing, we can get:
The essential ramifications here is that we knock the numbers by unambiguous \$\mathbb{N}\$. At start, we take the starting number, for our situation it is 1, we move once up and afterward once down. Then we do it two times, threefold, etc. So 1 3 2
as per my outline is one knock. At the closure \$\mathbb{N}\$ which is 2 here, we will hop it by 2 and make it low by 2. So it gets 2 5 12 7 4
. Here, expect \$\mathbb{N}_i\$ as the quantity of incrementation, before it was 1, presently it is 2. We get various sets, with various terms, however absolute number of terms we overcome this would be \$2 \mathbb{N}_i + 1\$. Presently, it will begin from 4, continue taking 3 leaps prior to arriving by three terms. By this, we get series featured by circles in that three-sided exhibit as:
1, 3, 2, 5, 12, 7, 4, 9, 20, 44, 24, 13, 7, 15, 32, 68, 144, 76, 40, 21, 11, 23, 48, 100, 208, 432, 224, 116, 60, 31, 16...
The series appear to be disparate, my particular inquiry this is the way to address this series in Numerical terms.
Challenge: Implement the algorithm which can build this series.
Scoring Criteria: It is ranked by fastest-algorithm so the answer with lowest time complexity is considered (time complexity is loosely allowed to be anywhere) but the program must have been running accurate result.