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)) }