Subwoofer connection

I've read quite a few posts on subwoofer connection for 2 channel amp/preamp. Here are different ways of connections from what I have read.
1. Using speaker wires.
a. Serial connection: from amp/preamp to the subwoofer in, and then from the subwoofer out to main speakers.
b. Parallel connection: from amp/preamp to both subwoofer and main speakers.
2. Using RCA cables, from the amp/preamp RCA out (or tape out) to RCA input of the subwoofer. Some people suggest to use just one wire from the left out from the amp/preamp to the left in of the subwoofer. This option is not possible for amps that do not have RCA out.

I have a subwoofer that allows those three different connections. However, I could not conclude which connection would be the best by reading posts. I might need to make my own decision for best result, but I would appreciate it if any of you have some thoughts on this.
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I use the parallel connection for my Abbys and NSM sub. Everything from the speaker taps. This way all speakers see the same signal. From the taps: spades to the speakers, bananas to the sub.
same here. I run the sub straight from my amp, like I would any speaker.
Yes, straight from your amp's outputs is best. It helps to give you the best "blending" between the sound of your main speakers with the sub. You get the same sonic signature that your amp imparts to your main speakers that way. If you use RCA's from your pre-amp, you will be be bypassing the amps sonic signature to the sub.
OK, but, what if you have an active sub with built in amp. I have the Rowland Synergy Ili Pre and Rowland 312 Amp feeding Avalon Indra's. If I run XLR cables from Pre to Sub, they will be on a different/separate input. The Synergy lli has 5 separate input switches. Obviously only one input can be selected at one time for playback (Balanced 2 channel - outs). What am I missing here?
The sub has it's own amp, like you said, but I'm just sending a signal not amplification. Amplification goes to the passive speakers.
Thanks for your comments.
The subwoofer has a 300W amp (from Keiga) and 12" woofer.
Currently, I have two different systems that I can use with the subwoofer.
1. 50W tube integrated amp with Tyler ref monitor
2. BAT vk60/vk30 with Tyler Linbrook systems

The ref monitor is rated 8ohm/88dB, and the linbrook is rated 4ohm/92dB. The subwoofer is rated 4ohm/89dB. As for the specs, wouldn't it matte if you connect both the main and subwoofer in parallel if their impedances are different (4ohm vs 8ohm)?

Many thanks.
The sub is not drawing any power from the amp, simply a signal. Once connected, your job is to blend them.
Got it. Took a look and the Rowland Synergylli has two sets of XLR outputs to amp. I suppose I simply connect a pair of XLR interconnects from the 2nd set of outputs from the Pre to the sub and make adjustments to blend for seamless integration. The Karma Ceramique Sub on the way seems to have a plethora of tuning options available. THX.