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

#*****************************************************************************80
#
## TETRAHEDRON_GRID_COUNT counts the grid points inside a tetrahedron.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    15 April 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of subintervals.
#
#    Output, integer NG, the number of grid points.
#
  ng = ( ( n + 1 ) * ( n + 2 ) * ( n + 3 ) ) // 6

  return ng

def tetrahedron_grid_count_test ( ):

#*****************************************************************************80
#
## TETRAHEDRON_GRID_COUNT_TEST tests TETRAHEDRON_GRID_COUNT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    15 April 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'TETRAHEDRON_GRID_COUNT_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  TETRAHEDRON_GRID_COUNT can count the points in a grid' )
  print ( '  with N+1 points on a side, based on any tetrahedron.' )

  print ( '' )
  print ( '     N        NG' )
  print ( '' )

  for n in [ 1, 2, 3, 4, 5, 10, 15, 20, 25, 50, 100 ]:
    ng = tetrahedron_grid_count ( n )
    print ( '  %4d  %8d' % ( n, ng ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TETRAHEDRON_GRID_COUNT_TEST:' )
  print ( '  Normal end of execution.' )
  return

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