math diversion: find difference between square of the sum of numbers {1 ,n} and the sum of the squares {1, n}

diff-squares.js

// 26 Dec 2022
// A diversion.

// Find the difference between the square of the sum of the numbers
// from 1 to n, and the sum of the squares from 1 to n.

function squareOfSum(n) {
  if (+n !== +n) {
    return 0
  }

  // square pyramidal numbers
  var sum = n * (n + 1) / 2

  return sum * sum;
}

console.group("squareOfSum")
console.log(
  squareOfSum(1),
  squareOfSum(2),
  squareOfSum(3)
)
console.groupEnd("squareOfSum")


function sumOfSquares(n) {
  if (+n !== +n) {
    return 0
  }

  // triangular numbers
  var i = 2
  var j = 3
  var k = (n * n * n) * i
  var s = (n * n) * j

  return (k + s + n) / (2 * 3)
}

console.group("sumOfSquares")
console.log(
  sumOfSquares(1),
  sumOfSquares(2),
  sumOfSquares(3)
)
console.groupEnd("sumOfSquares")


function diffSquares(n) {
  if (+n !== +n) {
    return 0
  }

  return squareOfSum(n) - sumOfSquares(n)
}

console.group("diffSquares")
console.log(
  diffSquares(1),
  diffSquares(2),
  diffSquares(3)
)
console.groupEnd("diffSquares")

/*
squareOfSum
  1 9 36
sumOfSquares
  1 5 14
diffSquares
  0 4 22
*/