After multiple test, I understant why it's work (but sadly not why this solution made that) :

A)
Explanation of what is bin() here https://www.programiz.com/python-programming/methods/built-in/bin

B)
I try to Bin numbers and count difference between Bin's size and Bin's size without 0 :

for i in range(20):
print("{} => {} => {}".format(i, bin(i), len(bin(i)) - len(bin(i).rstrip('0'))))

''' results
0 => 0b0 => 1
1 => 0b1 => 0
2 => 0b10 => 1
3 => 0b11 => 0
4 => 0b100 => 2
5 => 0b101 => 0
6 => 0b110 => 1
7 => 0b111 => 0
8 => 0b1000 => 3
9 => 0b1001 => 0
10 => 0b1010 => 1
11 => 0b1011 => 0
12 => 0b1100 => 2
13 => 0b1101 => 0
14 => 0b1110 => 1
15 => 0b1111 => 0
16 => 0b10000 => 4
17 => 0b10001 => 0
18 => 0b10010 => 1
19 => 0b10011 => 0

C) As you can see in last row, those Bin logic is the same that we want with letters:
you pop the first result for 0 and you got
[0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0]
Same as
[a, b, a, c, a, b, a, d, a, b, a, c, a, b, a, e, a, b, a]

Now why algorithmic logic Bin follows this process ...
I don't know if this sequence is known as that of Fibonacci or Padovan.
This must be related to the very logic of python operation.

With understandable formatting, this gives:

S(1) = "a"
S(2) = S(1) + "b" + S(1) => "a" + "b" + "a" => "aba"
S(3) = S(2) + "c" + S(2) => "aba" + "c" +"aba" => "abacaba"
S(4) => "abacabadabacaba"
...
S(26) = S(25) + "z" + S(25) => ??

abacaba(k) => S(26)[k]

whoa...