> 
>  V1:=vecptnsC(4,1,5);
V1 := [[[], [], [1, 1, 1, 1]], [[], [1, 1], [2]], [[], [1, 2], [1]],

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

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

>  nops(V1);
                                       9

>  add(vpw(V1[i]),i=1..nops(V1));
                                       1

> 
>  # There are 9 vector partitions of 4 with crank = 1 mod 5
>  # and total weight = 1.
> 
>  # vector partitions of 4 with crank = 2 mod 5
> 
>  V2:=vecptnsC(4,2,5);
V2 := [[[], [], [1, 1, 2]], [[], [1, 1, 1], [1]], [[], [2, 2], []],

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

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

>  nops(V2);
                                       7

>  add(vpw(V2[i]),i=1..nops(V2));
                                       1

> 
>  # There are 7 vector partitions of 4 with crank = 0 mod 5
>  # and total weight = 1.
> 
>  # vector partitions of 4 with crank = 3 mod 5
> 
>  V3:=vecptnsC(4,3,5);
V3 := [[[], [], [2, 2]], [[], [], [1, 3]], [[], [1], [1, 1, 1]],

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

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

>  nops(V3);
                                       7

>  add(vpw(V3[i]),i=1..nops(V3));
                                       1

> 
>  # There are 7 vector partitions of 4 with crank = 3 mod 5
>  # and total weight = 1.
> 
>  # vector partitions of 4 with crank = 4 mod 5
> 
>  V4:=vecptnsC(4,4,5);
V4 := [[[], [], [4]], [[], [1], [1, 2]], [[], [2], [1, 1]],

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

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