Download the sourcecode from GitHub.

Principal code of the new algorithm.

   
      //-- 12
      //-- +.+.+
      //-- ..+..
      //-- ++Q++
      //-- ..+..
      //-- +.+.+
      int twelfth = N % 12;

      int[] tmpBoard = new int[N + 4];
      Array.Clear(tmpBoard, 0, tmpBoard.Length);

      int nIndex = 0;

      // Diagonal knight from 2
      for (int i = 2; i <= N; i += 2)
        tmpBoard[nIndex++] = i;

      if (twelfth == 3 || twelfth == 9)
      {
        tmpBoard[0] = 0;
        tmpBoard[nIndex++] = 2;
      }

      for (int i = 1; i <= N; i += 4)
      {
        if (twelfth == 8)
        {
          tmpBoard[nIndex++] = i + 2;
          tmpBoard[nIndex++] = i;
        }
        else
        {
          tmpBoard[nIndex++] = i;
          tmpBoard[nIndex++] = i + 2;
        }
      }

      if (twelfth == 2)
      {
        for (int i = 0; i <= N; i++)
        {
          if (tmpBoard[i] == 1)
            tmpBoard[i] = 3;
          else if (tmpBoard[i] == 3)
            tmpBoard[i] = 1;
          if (tmpBoard[i] == 5)
            tmpBoard[i] = 0;
        }
        tmpBoard[nIndex++] = 5;
      }

      if ((twelfth == 3) || (twelfth == 9))
      {
        for (int i = 0; i <= N; i++)
          if (tmpBoard[i] == 3 || tmpBoard[i] == 1)
            tmpBoard[i] = 0;
        tmpBoard[nIndex++] = 1;
        tmpBoard[nIndex] = 3;
      }

      nIndex = 0;

      for (int i = 0; i < tmpBoard.Length; i++)
        if (tmpBoard[i] != 0 && tmpBoard[i] <= N)
          m_Board[nIndex++] = tmpBoard[i] - 1;