FUNCTION:  partitions[ptnCC] - partitions with part diff at least 3
 
CALLING SEQUENCE:  ptnCC(ptn)
 
PARAMETERS:    ptn -  partition
 
GLOBAL VARIABLES: NONE
SYNOPSIS:  
   Returns true if ptn is a partition in which difference between parts
   is at least 3.
                    
EXAMPLES:  
                    
> with(combinat):
> with(partitions):
> with(qseries):
> ptn1:=[1,3,6];
                               ptn1 := [1, 3, 6]

> ptnCC(ptn1);
                                     false

> ptn2:=[1,6,9];
                               ptn2 := [1, 6, 9]

> ptnCC(ptn2);
                                      true

> ptns:=partition(9):
> ptns1:=select(ptnCC,ptns);
                     ptns1 := [[3, 6], [2, 7], [1, 8], [9]]

> nops(ptns), nops(ptns1);
                                     30, 4

> GENFUNC:=1+add(nops(select(ptnCC,partition(n)))*q^n,n=1..30);
               30       29       28       27       26       25       24
GENFUNC := 66 q   + 58 q   + 52 q   + 46 q   + 41 q   + 36 q   + 32 q

           23       22       21       20       19       18       17       16
     + 28 q   + 25 q   + 22 q   + 19 q   + 17 q   + 15 q   + 13 q   + 11 q

           15      14      13      12      11      10      9      8      7
     + 10 q   + 8 q   + 7 q   + 6 q   + 5 q   + 4 q   + 4 q  + 3 q  + 3 q

          6      5    4    3    2
     + 2 q  + 2 q  + q  + q  + q  + q + 1

> prodmake(GENFUNC,q,30,list);
[-1, 0, 0, 0, -1, 0, -1, 0, -1, 1, -1, 0, -1, 1, -2, 1, -2, 1, -2, 2, -3, 
  3, -3, 3, -5, 5, -6, 5, -8]

DISCUSSION:  ptn1 is not such a partition, ptn2 is 
             Of the 30 partitions of 9 only 4 satisfy the condition
             The generating function does not look like a nice product
                    
SEE ALSO: ptnDP, ptnRR