Smart home with ws2812b led band

Hi people! I am new to Arduino so this is my first project.I want to create underglow for the staircase of my home using Arduino.In total I have 15 stairs.I decided to use ws2812b rgb band (beacuse is a digital rgb band and 1 pin to control) ,and 2 PIR sensors(one on top of the staircase and other on bottom of staircase) (OPTIONAL --> [[But one thing it bothers me.I want to control whole rgb,when I want with an app (created by me) via ethernet port module,but I don't know if I have enough pins on Arduino.]]Also should I add a 9V battery to keep the Arduino on during a power failure? Cause I want to code an clock so the rgb band changes color/brightness during the hours.
Can someone create a wiring diagram?

Yes. You can. Adafruit website has a lot of good info on that.

By the way, there is no way a tiny 9V battery will power 15 steps of lighting. If you want to keep track of time, attach an RTC module.

also how I can connect 2 montion sensors (HC-SR501) to use individual pins ,so I can have animations for going upstairs and going downstairs.Should I use a arduino mega for this project? or a arduino UNO is enough,cause I need 13 meters of Ws2812b

It depends on the number of LEDs. Different strips have a different number of LEDs per-meter. Each pixel (LED) needs 3 bytes of RAM and some RAM will be used by other parts of your program and possibly by the LED library.

Ethernet might eat-up lots of RAM.

Addressable LEDs need quite a bit of processing power by themselves. Of course, most people have some kind of input controlling the LEDs so the processor is usually doing "something else" too. You may have to pause everything while you run the LED sequence but the additional software still takes some flash and RAM space.

I would also recommend reading the Adafruit Guide and doing some experiments before trying to build the thing.

The sensors will probably be simple so I'd make sure you can control the LEDs the way you want first, and then work on the sensors separately before putting everything together.

Work on the clock separately too. I think most real-time clock modules have their own back-up battery so you don't loose time when power goes out.

...I'd say a real time clock and/or Ethernet make this more of an "intermediate" or "advanced" project. Just the sensors and LEDs might qualify as a "beginner project".

What about a Bluetooth module + an app?(I have a android phone so I can make it)

Yes they have a external battery

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