You don't need to list them.  You can think through them.

If you don't use any quarters, you can use from 0 through 6 dimes
and the rest, if any, in nickels. That's 7 ways.

If you use 1 quarter you can make the remaining 35 cents by
using from 0 through 3 dimes and the rest in nickels. That's
4 ways.

If you use 2 quarters you can make the remaining 10 cents with
either 1 dime or 2 nickels. That's 2 ways.

Answer 7+4+2 = 13 ways.

Edwin