This challenge takes place on the snub square tiling.

Start by choosing any triangle, and color it \$c_1\$.Next, find all tiles which touch this triangle at any vertex, and color them \$c_2\$. Next, find all tiles which share a vertex with any \$c_2\$-colored tile, and color these \$c_3\$.Continue this process ad infinitum.

Illustration

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Initial terms

The sequence begins

  a(1) = 1  a(2) = 9  a(3) = 21  a(4) = 35

Notice:

• a(1) = 1 corresponds to the red triangle;
• a(2) = 9 corresponds to the number of tiles in the second, orange layer;
• a(3) = 21 corresponds to the number of tiles in the third, green layer; and so on.

(Note, this sequence is now in the OEIS; OEIS sequence A296368 is closely related.)

Challenge

Your goal is to write a program that takes in a positive integer n and returns the number of tiles that are colored \$c_n\$, (i.e. the number of tiles in the \$n\$-th layer.) This is a code-golf challenge, so the shortest code in bytes wins.