3-4-5

5-12-13

7-24-25

9-40-41

11-60-61

13-84-85

15-112-113

17-144-145

etc.

The short side increases by 2 in each progression. The long side and the hypotenuse also increase by a fixed measure: The difference between the two preceding sides, plus 4.

ie:

difference betwen 0 and 4 is 4. 4 plus 4 = 8. 4 plus 8 = 12

difference between 4 and 12 is 8. 8 plus 4 = 12. 12 plus 12 = 24

difference between 12 and 24 is 12. 12 plus 4 = 16. 24 plus 16 = 40

difference between 24 and 40 is 16. 16 plus 4 = 20. 40 plus 20 = 60

difference between 40 and 60 is 20. 20 plus 4 = 24. 60 plus 24 = 84

difference between 60 and 84 is 24. 24 plus 4 = 28. 84 plus 28 = 112

difference between 84 and 112 is 28. 28 plus 4 = 32. 112 plus 32 = 144

etc.

The hypotenuse also increases by the difference between the two preceding, plus 4.