Electronic – LEDs blinking circuit problem

I must confess I never tried this. But the series resistor has an important role: it is there to limit the current through the LED. If there's no resistor, the current may be limited in the end to a value which is too high for the LED or for the driver transistor. Theoretically you should graphically add the U-I characteristics of the diodes and the LED, and see on the the resulting characteristic what's the current for your Vcc value. But the main problem is that this current cannot be reliable predicted, since the U-I catalog characteristics of the diodes and LED give you an typical curve, and this curve will also shift with the temperature.

So while it may work, I wouldn't count on it working in every instance. But you may have some help from an unexpected place: the IC driving your LEDs. Sometimes the digital outputs have internal resistors or other ways to limit the output current, in order to avoid overloading them. So check the spec sheet for your attiny2313.

In the second 'for' loop, i is immediately not <1, so the loop never executes.

for(int i =7; i<1; i--)

should say

for(int i =7; i>=0; i--)