Tribonacci word
Hello there! Do you know what a Fibonacci sequence is?
No? Let me explain. In a Fibonacci sequence, each number is the sum of the two numbers that came before it. So it goes like this:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377
Now, let's talk about a Tribonacci sequence. It's a bit like a Fibonacci sequence, but instead of adding the two preceding numbers, you add the three preceding numbers.
So, in a Tribonacci sequence, the first three numbers are 0, 0, and 1. Then, each subsequent number is the sum of the three numbers that came before it.
0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927...
Now, a Tribonacci word is made up of the letters A, B, and C. It starts with the letter A, followed by the letter B, and then the letter C. After that, it follows the same pattern as the Tribonacci sequence. So the next letter is the sum of the three preceding letters.
Here's an example:
A, B, C, ABC, BCA, CAB, ABCBCA, BCACAB, CABABCBCA, ABCBCACAB...
Got it? So a Tribonacci word is just like a Tribonacci sequence, but with letters instead of numbers. That's it!
No? Let me explain. In a Fibonacci sequence, each number is the sum of the two numbers that came before it. So it goes like this:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377
Now, let's talk about a Tribonacci sequence. It's a bit like a Fibonacci sequence, but instead of adding the two preceding numbers, you add the three preceding numbers.
So, in a Tribonacci sequence, the first three numbers are 0, 0, and 1. Then, each subsequent number is the sum of the three numbers that came before it.
0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927...
Now, a Tribonacci word is made up of the letters A, B, and C. It starts with the letter A, followed by the letter B, and then the letter C. After that, it follows the same pattern as the Tribonacci sequence. So the next letter is the sum of the three preceding letters.
Here's an example:
A, B, C, ABC, BCA, CAB, ABCBCA, BCACAB, CABABCBCA, ABCBCACAB...
Got it? So a Tribonacci word is just like a Tribonacci sequence, but with letters instead of numbers. That's it!