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3 green leds (button leds) are connected in series. Using 12 volts car battery and a simple current limiting using resistor, avoiding constant current. Good heatsink is used. No standard spec is available for these leds, some say 3.7 Volts and 750 mA . What is the resistor value. Resistor value can be calculated by subtracting led voltages from supply voltage and dividing by current, but that's not complete design with these leds varying specs.
To be precise, just set a laboratory power supply to current-limit at 0.75A. Then, put each LED across it. The power supply will clamp to the actual forward voltage of the LED (i.e. you don't have to 'assume' or 'guess' it's 3.7V) In so far as the actual current handling of the LED, you can check datasheets for similar packages (I recognize this, it's available from many manufacturers) They'll all be about the same.
If you really want to use a resistance, calculate it for just below 750mA; say 500mA. That will address the problem of the varying specs. If the brightness is not enough, just decerase the resistance. The problem with resistance is that it needs to have a big power rating (at least 6W as per the asumptions.)
Maybe you can check on a LED driver IC. What these circuits do is maintaining a constant current regardless of the Vf of the LED. Using a LED driver is much more complicated than a using resistance but it's also much more efficient.
