FUNCTION:  partitions[overptns] - Overpartitions of n
 
CALLING SEQUENCE:  overptns(n)
 
PARAMETERS:     n  -  nonnegative integer
                   -  
 
GLOBAL VARIABLES:                     
SYNOPSIS:  
   overptns(n) generates a list of the overpartitions of n
   Here an overpartition is an element of DP X P
   where DP is set of partitions into distinct parts and
   P is set of unrestricted partitions of n.
                    
EXAMPLES:  
                    
> with(combinat):
> with(partitions):
> ovptns4:=overptns(4);
ovptns4 := [[[], [1, 1, 1, 1]], [[], [1, 1, 2]], [[], [2, 2]], [[], [1, 3]],

    [[], [4]], [[1], [1, 1, 1]], [[1], [1, 2]], [[1], [3]], [[2], [1, 1]],

    [[2], [2]], [[1, 2], [1]], [[3], [1]], [[1, 3], []], [[4], []]]

> nops(ovptns4);
                                       14

> for ovptn in ovptns4 do 
> print(ovptn);
> od:
                               [[], [1, 1, 1, 1]]

                                [[], [1, 1, 2]]

                                  [[], [2, 2]]

                                  [[], [1, 3]]

                                   [[], [4]]

                                [[1], [1, 1, 1]]

                                 [[1], [1, 2]]

                                   [[1], [3]]

                                 [[2], [1, 1]]

                                   [[2], [2]]

                                 [[1, 2], [1]]

                                   [[3], [1]]

                                  [[1, 3], []]

                                   [[4], []]

DISCUSSION:  
   There are 14 overpartitions of 4. 
   They are listed above.
                    
SEE ALSO:  overptncrank, overptnrank