title: Friends Pairing Problem 2
signature: function friendsPairingProblem2($n) {
test_code: <?php
  
  
  // SOLUTION CODE 
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  function validateSolution($actual, $expected){
      return serialize($actual) == serialize($expected);
  }
  
  function driver($n, $expected){
      try{
        if (validateSolution(PLACEHOLDER_FN_NAME($n), $expected)){
          return "PASSED";
        }
        return "FAILED";
      }
      catch (Exception $exception_obj) {
        return get_class($exception_obj);
      }
  }
  
  function main(){
      printf("TEST-0...%s\n",driver(
        24, 
        17492190577600));
      
      printf("TEST-1...%s\n",driver(
        1, 
        1));
      
      printf("TEST-2...%s\n",driver(
        29, 
        101990226254706560));
      
      printf("TEST-3...%s\n",driver(
        3, 
        4));
      
      printf("TEST-4...%s\n",driver(
        14, 
        2390480));
      
  }
  
  main();
  ?>
source_py: def friends_pairing_problem_2(n):
      (a, b, c) = (1, 2, 0)
      if (n <= 2):
          return n
      for i in range(3, (n + 1)):
          c = (b + ((i - 1) * a))
          a = b
          b = c
      return c
source_cpp: int friends_pairing_problem_2(int n) {
    int a = 1, b = 2, c = 0;
    if ( n <= 2 ) {
      return n;
    }
    for ( int i = 3;
    i <= n;
    i ++ ) {
      c = b + ( i - 1 ) * a;
      a = b;
      b = c;
    }
    return c;
  }