Why not some linebreaks to make it readable

As it reads

1. Select each number and it's index (0 based position) in the list
2. If current number equal to previous number in List (ignoring index 0 because no previous number) add null entry to new returned enumerable
3. Else [Implied If current number not equal to previous number - i.e. beginning of new sequence] Skip(i) amount of elements up to current position and Take() the next value in this sub-enumerable While() next value is equal to current value in the outer enumerable and Sum() them together
4. Filter out nulls
5. Select values
6. Convert to List for return type

{1,4,4,4,0,4,3,3,1} becomes:
{1,12,null,null,0,4,6,null,1}

I'm confused how this solution doesn't produce {1,12,8,4,0,4,6,3,1} for Input: {1,4,4,4,0,4,3,3,1} but I couldn't figure out any one liner so what do I know.

Is it possible to get a break down of this solution please?

I knew it will be a one liver through Linq meanwhile my solution is like tens of lines lol

Same here, spent about a day trying to solve it.

im in awe, i pondered over this for a while

Linq is indeed a very effective technology

People who master the arts of Linq see the world in a different perspective ^^

You are right.
It should be done in two steps:

res[i] = res[i - 1] - res[i - signature.Length - 1];
res[i] += res[i - 1];

Otherwise I still like this solution better, than those which sum n-times over the n previous elements.

res[i - 1] * 2 could possibly overflow the double type.