Start with the total of single rectangles eg: a ten stick will have ten single rectangles. Every time you increase the size of the rectangle by one,(to a double or triple or quadruple etc) starting with the total of single rectangles, you decrease the number of rectangles by one.
Eg: for a ten stick you will have:
10 singles
9 doubles
8 triples
7 quadruples
6 '5ers'
5 '6ers'
4 '7ers'
3 '8ers'
2 '9ers'
1 '10er'
Total: 55
The overall pattern is:
10 stick: 55
9 stick: 45
8 stick: 36
7 stick: 28
6 stick: 21
5 stick: 15
4 stick: 10
3 stick: 6
2 stick: 3
1 stick: 1
Each time you increase the number of single rectangles in a stick by 1, you add the number of single rectangles in the new stick to the overall number of rectangles in the original stick.