Arduino and several leds

Step back and think of the true requirements. You want the lamp to come on softly when you turn it on, and go off softly when you turn it off. Don't complicate things by dictating where in all this power must be switched.

You have a microcontroller, so the on and off signals can be inputs to it instead of physically interrupting power. The micro can then decide what to do about it and eventually switch off the power or go into sleep mode such that the power draw is so low as to be irrelevant. A modern micro in sleep mode with the right power supply can draw far less current than the average clock, for example.

A arduino is a lot of fancy stuff and layers of abstraction wrapped around a microcontroller dumbed down for the masses. Whether that can go to very low power I don't know, but a bare micro certainly can. If not, you can use a micro directly (it's really not that hard, just seems intimidating at first, which is what the arduino caters to), or maybe have the arduino physically turn off power when it is done with the dimming via a relay or something.

The on/off button would force the relay on with the micro having the ability to keep it on thereafter. On power up, the micro knows the lamp is being turned on. It drives the enable to keep the relay on after the on/off button is released, then goes thru the soft start sequence. When the button is detected while on, the micro goes thru the soft off sequence, then stops forcing the relay on, which will completely cut power.

When you multiplex a large number of LEDs individually the common way is to use an N x M matrix. The time is divided in N steps, in each step you activate one of the N row lines, and the column lines that correspond of the LEDs you want to enable. Note that the row lines can each carry M times the LED current, which asks for some buffering. Each LED is on only 1/N of the time, so to keep the normal brightness you must increase the current N-fold. Most LEds don't like this. Charlieplexing is not practical in ths situation because of the large currents involved.

From your question I understand that you want to enable only 1 LED at a time? In that case there is nothing wrong with Charlieplexing. A uC with 31 I/O pins can drive 900 LEDs. Sounds like the consruction will be a nightmare...

Update 5 years later: Normal multiplexing or Charlieplexing is nice when you have too much time at hand, but when I had to control 100's of LEDs now I would buy a long strip of WS2801 LEDs.