If we use no quarter or dimes, then we can use from 0 through 5 nickels,
and the rest pennies.  That's 6 ways.

If we use no quarter and 1 dime, then we can make the remaining 18 cents 
using from 0 through 3 nickels, and the rest pennies.  That's 4 ways.

If we use no quarter and 2 dimes, then we can make the remaining 8 cents
using 0 or 1 nickel, and the rest pennies.  That's 2 ways.

If we use a quarter, then we can only make the remaining 3 cents
using 3 pennies.  That's 1 way.

Total: 6+4+2+1 = 13 ways.

Edwin