Electrical – Right power supply for 5050 led strip

There are more than a few ways to drive LEDs directly from AC mains, among them:

In 1 and 2, half of the LEDs will be driven during the mains' positive half-cycle, and the other half during the negative half-cycle.

With 50 Hz mains, each string will half-wave rectify the mains and flash at 50Hz (i.e. be on for around half the time), which is visually detectable and annoying, so that approach will be abandoned.

In 3 and 4, the mains is full-wave rectified, so the string will flash at 100Hz, which is visually undetectable and, therefore. acceptable.

For 24V 5050 strips to be connected across 240V mains, no current limiters will be needed and all that'll be required is to connect 10 of then in series across the 240V mains like this:

Likewise, for 12V strips to be connected across the main, 20 will need to be connected in series then connected across the 240V mains.

LED strips work at \$12\, \mathrm{V}\$, but the individual chips do not. They are connected in groups of three with one series resistor. Voltage drop of one LED is around \$3.6\, \mathrm{V}\$, so the current is \$\dfrac{0.24}{3.6}\cong 65\, \mathrm{mA}\$. For 30 blocks, it is \$30\cdot 65 \cong 2\, \mathrm{A}\$.

LM2596 is quite ancient, you could do better with something like TPS54340 or even better, with synchronous buck regulator likeLT8614. Newer chips have higher switching frequecies, which means that you can use smaller inductors with fatter wire and also smaller capacitors.

With only one block attached, it will work just fine (although less advanced regulators will have lower efficiency).

If you connect too much LEDs, you will overload and overheat the regulator and it will employ its overtemperature protection.

Edit: LEDs are grouped by 3 like this: