Project Euler, problem 463

f :: Integer -> Integer
f 1 = 1
f 3 = 3
f n | mod n 2 == 0        = f n1
    | mod (n - 1) 4 == 0  = 2 * (f (2 * n2 + 1)) - (f n2)
    | mod (n - 3) 4 == 0  = 3 * (f (2 * n2 + 1)) - 2 * (f n2)
  where
    n1 = div n 2
    n2 = div n 4

s :: Integer -> Integer
s n = sum . map f $ [1..n]