Using a microcontroller to turn on LED strip
You're nearly there, a couple of things though:

The base resistor calculation ins't correct - remember you only need 1.6mA according to your calculations (the collector current is separate).
Looking at the datasheet, the minimum gain is 1000, and maximum base-emitter voltage is 2.5V, which means we need to adjust the calculations, 1.6mA will do for the base current (always good to have extra for a switch as the gain drops at saturation) but we need to use 2.5V rather than 1.3V for worst case (it's better to use worst case/maximum values to design with, though looking at the graph it seems the extra Vbe is unlikely at this current, so somewhere between the two figures below should be okay):

So:

(3.3V - 2.5V) / 1.4mA = 570&Omega;

or

(3.3V - 1.5V) / 1.4mA = ~1.2k&Omega;

This should work okay, but is not the most efficient way to do things - the transistor dissipation will be at least 0.4A * Vce(sat) which is about 0.4A * 0.75V = 0.3W, plus your R-pi needs at least a couple of mA or so to drive it.
A modern logic level MOSFET can be much smaller, be driven with (almost) no current) and have almost no dissipation. Here is an example part, the FDC637BNZ , chosen at random from thousands at Farnell: