Concentric rings on a snub square tiling 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

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.
Ruby, 26 bytes



-&gt;n{~-n*12-496/4**n%4+1/n}


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Revised version adding 1/n and subtracting 496/4**n%4 to get the +1,-3,-3,-1 offset for the first 4 terms.

Ruby, 32 bytes



-&gt;n{n&gt;4?~-n*12:[0,1,9,21,35][n]}


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After 4, the sequence settles down to (n-1)*12. See diagram below (the equilateral triangles have been distorted into 45 degree isosceles triangles and the entire diagram rotated 45 degrees, but it remains topologically equivalent.)