Concentric rings on a snub square tiling
Ruby, 26 bytes



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


Try it online!

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]}


Try it online!

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.)