Full Example — Sequence to Compute n * n

The square $n*n$ can be computed using the following sequence:

$$ n^2 = n + 2 \sum_{i=0}^{n-1} i$$

In scala:

def square(x: Int): Int = {
  def sq(y: Int): Int = y match {
    case 0 => 0
    case 1 => 1
    case _ => val y2 = ((1 to (y - 1)).reduceLeft( _ + _ ))
              y + y2 + y2
  }
  val z = Math.abs(x)
  sq(z)
}

for (i < - -20 to 20) {
  println(square(i))
}