When you run LEDs on AC, they only light during half the AC cycle, so you get flicker. Also you will shorten the life of the LEDs unless the 2 parallel strings are connected with opposite polarity.
Here is a filtered rectifier circuit:
Connect AC to the two bridge rectifier leads marked ~, and you get DC voltage from the + and -.
Make sure you match the polarity of the capacitor to the bridge rectifier (+ to +, - to -) or you will have an exploding capacitor. The capacitor "fills in" the gaps between the peaks so you won't get any flicker.
Pay attention to GRJ's advice about the filtered rectifier circuit increasing the DC output voltage and requiring a bigger resistor. He's smarter than most of us with half his brain tied behind his back. 
I was about to question your entry of 120ma in the LED calculator, as most LEDs only draw 20ma. You must be using the "high power" LEDs that do draw 120ma. That's going to be one bright tower!! Pictures, please!
Bob
