How do I interpret the formula for OEIS A334742 (https://oeis.org/A334742), which is given as:
$$a(A033638(n)) = a(A002620(n)) \,\,\mathrm{for}\,\, n > 1.$$
Since
$$A002620(n)= \Bigl\lfloor\frac{n^2}{4}\Bigr\rfloor$$
and
$$A033638(n) = A002620(n)+1 = \Bigl\lfloor\frac{n^2}{4}\Bigr\rfloor+1,$$
it seems we have:
$$a( \Bigl\lfloor\frac{n^2}{4}\Bigr\rfloor+1) = a( \Bigl\lfloor\frac{n^2}{4}\Bigr\rfloor) \,\,\mathrm{for}\,\, n > 1.$$
The sequence $\left\{\left\lfloor\frac{n^2}{4}\right\rfloor\right\}=\{0,1,2,4,6,9,12,16,20,25,\ldots\}$
So your final line tells us: $$\begin{align} &a(1)=a(0)\\ &a(2)=a(1)=a(0)\\ &a(3)=a(2)=a(1)=a(0)\\ &a(5)=a(4)\\ &a(7)=a(6)\\ &a(10)=a(9)\\ &a(13)=a(12)\\ &a(17)=a(16)\\ &a(21)=a(20)\\ &a(26)=a(25) \end{align}$$
That is, it tells us some members of $a(n)$ are equal to other members.
Note that it says nothing about certain members like $a(8)$. And it doesn't say anything about how $a(3)$ and $a(4)$ relate to each other (for example).