The L polyomino of size 4m+2 is odd

In my paper Tiling Rectangles and Half Strips with Congruent Polyominoes, I asked if the L polyomino of size n , where n ≡ 2 mod 4 , can tile a rectangle using an odd number of tiles. Philippe Rosselet has shown that the answer is "yes".

L₆ tiles a 14 × 21 rectangle:

L₁₀ tiles a 22 × 55 rectangle:

L₁₄ tiles a 30 × 105 rectangle:

In general, L_4m+2 tiles an (8m + 6) × (4m + 3)(2m + 1) rectangle.

Charles Jepsen has independently found a similar tiling, see [1, Figure 5].

Reference:
[1] Charles H. Jepsen, Lowell Vaughn and Daren Brantley, Orders of L-shaped Polyominoes, Journal of Recreational Mathematics 32 (2003-2004), no. 3, pp. 226-231.

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