Haar transform definition I am trying to understand Haar transform of simple vector of numbers.

Some references I found say, that first level transform of $ X = (4,6,8,10,13,9,3,3)$ will be $\sqrt{2}(5,9,11,3, -1,-1,2,0)$. Others say, it will be $(5,9,11,3,-1,-1,2,0)$.

Which one is true? Or are they both correct in some way and am I missing something?

And important question, which one do I use when I am performing Haar transform on image and this vector represents one row/column of pixels in image?
The only difference between the two transform results is a gain factor.  The transform should have the same energy as the original data sequence, so we can use that to check for the right result.  The energy of $X$ is-

$$
\sum X^2 = 484
$$
$$
\sum (5,9,11,3,−1,−1,2,0)^2 = 242
$$
$$
\sum (\sqrt{2}(5,9,11,3,−1,−1,2,0))^2 = 2\sum (5,9,11,3,−1,−1,2,0)^2 = 484
$$
This shows that of the two possible transforms, $\sqrt{2}(5,9,11,3,−1,−1,2,0)$ has the right energy and is thus the right choice.