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Can L tilings be created for L shaped structure (such that the L tilings are in fact trominoes). It seems to not be such a simple question to answer! Though their may be multiple ways of answering the same.

HelloPeople
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    Have you succeeded to find such a tiling for $n=3,5$? – Berci Feb 09 '21 at 23:42
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    The title of this question could be improved by making it more specific to the content question. – Galen Feb 09 '21 at 23:53
  • I guess we should include other kinds of bigger tiles (typically certain rectangles, e.g. $2\times 3$, or more general L kinds of shapes) in the induction hypothesis. – Berci Feb 09 '21 at 23:55
  • @Berci, yes in fact this is possible for all n>=1, which is what we have to prove. You can find such tillings relatively easily for n =3,5 ,etc – HelloPeople Feb 10 '21 at 02:45

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For the case when $n$ is odd

It is easy to divide any $3\times 2k$ rectangle into tiles.

So, divide your large L-shape into the following shapes. A and C form a border of width $3$ along the longest sides of the large L-shape.

A. Two $3\times (2n-6)$ rectangle3

B. Two $3\times (n-3)$ rectangles

C. A new L-shape with $n$ replaced by $3$

D. A new large L-shape with $n$ replaced by $n-3$.

You can now apply induction.