Despite what it says in the description, there are 16 segments per rope, not 20. Also worth noting if you're using the FastLED library, the color order is BRG. Here's a video of the FastLED demo sketch running on 7 ropes (112 total segments):

https://youtu.be/8af9VsmrW7I

Is is possible to get longer lengths of this?

Can this item be cut just like the led strips?

These are not quite what I expected. They are very pretty and quite bright, but they are much much thicker than a normal LED strip or even a rope light. The suggested FastLED library works great. I adapted the included Cylon (code below) sketch to produce a quick video demo.
https://youtu.be/wTi-pQ5de3Q Some notes: The red stripe wire is +24v, the middle wire is 5v data, the other end wire is ground. Be sure to tie the 24v ground to arduino ground. Be careful to limit how tightly you bend these. The data line seems to be sensitive and some LED's can get stuck if the bend is too tight, see the video for an example of this effect.

#include "FastLED.h"

// How many leds in your strip?
#define NUM_LEDS 20 

// For led chips like Neopixels, which have a data line, ground, and power, you just
// need to define DATA_PIN.  For led chipsets that are SPI based (four wires - data, clock,
// ground, and power), like the LPD8806, define both DATA_PIN and CLOCK_PIN
#define DATA_PIN 7

// Define the array of leds
CRGB leds[NUM_LEDS];

void setup() { 
    Serial.begin(57600);
    Serial.println("resetting");
    LEDS.addLeds<UCS1903,DATA_PIN,RGB>(leds,NUM_LEDS);
    LEDS.setBrightness(84);
}

void fadeall() { for(int i = 0; i < NUM_LEDS; i++) { leds[i].nscale8(250); } }

void loop() { 
    static uint8_t hue = 0;
    Serial.print("x");
    // First slide the led in one direction
    for(int i = 0; i < NUM_LEDS; i++) {
        // Set the i'th led to red 
        leds[i] = CHSV(hue++, 255, 255);
        // Show the leds
        FastLED.show(); 
        // now that we've shown the leds, reset the i'th led to black
        // leds[i] = CRGB::Black;
        fadeall();
        // Wait a little bit before we loop around and do it again
        delay(10);
    }
    Serial.print("x");

    // Now go in the other direction.  
    for(int i = (NUM_LEDS)-1; i >= 0; i--) {
        // Set the i'th led to red 
        leds[i] = CHSV(hue++, 255, 255);
        // Show the leds
        FastLED.show();
        // now that we've shown the leds, reset the i'th led to black
        // leds[i] = CRGB::Black;
        fadeall();
        // Wait a little bit before we loop around and do it again
        delay(10);
    }
}

The video is a must-watch for Feldi's detailed information and enthusiasm. While the product description currently says "nonaddressable", Feldi demonstrates animation on the strip. She explains that in fact,

• each group of 3 LEDs along the strip is controlled by a UCS1903 chip

• this protocol is available in the FastLED library (alongside WS2812, APA102, etc)

This appears to be a 5v protocol, so I'd connect the ground of the 24vdc power supply to the Arduino ground, and use a digital pin to connect to the strip's data line. I'd also add that there are likely cutlines on the strip every 0.1m (3.94 in).

One more thought: I realize you probably don't have any control over this (pardon the pun), but I'd really like to see this with programmable LEDs ("Dot-Star"?) so we could have more control. I have a use in mind that would likely have two ropes, but they'd need to be "coordinated". The "neon-effect" of the sheathing would be really beneficial in this use, although I certainly don't need the waterproofing.

The datasheet (UCS 1903) seems to be for the chips used to control individual LEDs. At the moment, I see nothing on the "care and feeding" (i.e., pin hookup) of the rope. I hope we can get this corrected. From the pictures, the connectors have 3 pins. Obviously, one is +24V and one is "GND", but what's the third one used for, and which is which?

Would love a data sheet on the physical properties of the product. What is the minimum bend radius of the strip? Do you supply pins for cutting/extending strips?

Can this be cut for a shorter segment?