#! /usr/bin/env python
#
def pyramid_square_num ( n ):

#*****************************************************************************80
#
## PYRAMID_SQUARE_NUM returns the N-th pyramidal square number.
#
#  Discussion:
#
#    The N-th pyramidal square number PS(N) is formed by the sum of the first
#    N squares S:
#
#      S(I) = I^2
#
#      PS(N) = sum ( 1 <= I <= N ) S(I)
#
#    By convention, PS(0) = 0.
#
#    The formula is:
#
#      PS(N) = ( N * ( N + 1 ) * ( 2*N+1 ) ) / 6
#
#    Note that geometrically, this pyramid will have a square base.
#
#  Example:
#
#    0    0
#    1    1
#    2    5
#    3   14
#    4   30
#    5   55
#    6   91
#    7  140
#    8  204
#    9  285
#   10  385
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    14 August 2014
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer  N, the index.
#    0 <= N.
#
#    Output, integer PYRAMID_SQUARE_NUM, the N-th 
#    pyramid square number.
#
  value = ( n * ( n + 1 ) * ( 2 * n + 1 ) ) / 6

  return value

def pyramid_square_num_test ( ):

#*****************************************************************************80
#
## PYRAMID_SQUARE_NUM_TEST tests PYRAMID_SQUARE_NUM.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    04 December 2014
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'PYRAMID_SQUARE_NUM_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  PYRAMID_SQUARE_NUM computes the pyramidal square numbers.' )
  print ( '' )
 
  for n in range ( 1, 11 ):
    print ( '  %2d  %6d' % ( n, pyramid_square_num ( n ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'PYRAMID_SQUARE_NUM_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  pyramid_square_num_test ( )
  timestamp ( )