Controlling/Strobing 60 LED'S

Do you know what voltage you are going to use to drive them?

You can put LED's in series as long as the sum of the voltage drops (Forward Voltage) is less than the power supply voltage. Since these seem to have about a 3V drop you can't put them in series if you are driving them with 5V but can put 3 in series if you drive them with 12V.

Each set of series LED's needs a current limiting resistor. You figure out the resistance by taking the supply voltage, subtracting the voltage drop of the LED (sum of the voltage drops if LED's are in series) and dividing that voltage by the current (20 mA in your case) to get ohms.

5V - 3V = 2V, 2V / 0.020 A = 100 Ohms
12V - (3V+3V+3V) = 3V, 3V / 0.020 A = 150 Ohms