Contrast statement

[Miracle]

Hi there.

Can someone please explain to me about the contrast statement? 

For example, to test the linear/quadratic/cubic trend of a 4-level variable, the contrast statements will be

Linear -3 -1 1 3 
Quad 1 -1 -1 1 
Cubic -1 3 -3 1.

I just can't get my head around how it is -3 -1 1 3 for linear, 1 -1 -1 1 for quadratic and -1 3 -3 1 for cubic. I only understand they need to sum up to zero.

Thank you heaps.

[data_null__]

Run this program.

data op;
   input linear quadratic cubic;
   x + 1;
   cards ;
-3  1 -1
-1 -1  3
 1 -1 -3
 3  1  1
;;;;
   run;
proc print;
   run;
proc sgplot;
   pbspline x=x y=linear;
   pbspline x=x y=quadratic;
   pbspline x=x y=cubic;
   run;