count_dp

function count(arr, arrLength, target) {
  if (target === 0)
    return 1;
  
  if (target < 0 || (arrLength <= 0 && target >= 1))
    return 0;
  
  return count(arr, arrLength - 1, target) + count(arr, arrLength, target-arr[arrLength - 1]);
}

function count_dp(arr, arrLength, target) {
  var table = new Array(arrLength + 1);
  
  for (var i = 0; i <= table.length; i++) {
    table[i] = 0;
  }
  
  table[0] = 1;
  
  for (var k = 0; k < arrLength; k++) {
    for (var j = arr[k]; j <= target; j++) {
      table[j] += table[j - arr[k]];
    }
  }
  
  return table[target];
}

var arr = [1, 2, 3];


console.log(count_dp(arr, arr.length, 4));