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.
The sequence begins
a(1) = 1 a(2) = 9 a(3) = 21 a(4) = 35
a(1) = 1corresponds to the red triangle;
a(2) = 9corresponds to the number of tiles in the second, orange layer;
a(3) = 21corresponds to the number of tiles in the third, green layer; and so on.
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.