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25-Diamond I
October 6, 2022

Are you looking for something like this:

Werner_E_1-1665093067340.png

 

 

24-Ruby IV
October 7, 2022
25-Diamond I
October 7, 2022

Yes, these are well know generalizations of Fibonacci

Extension to negative integers

https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Extension_to_negative_integers

as well of summing up more than two successive numbers - they are called Tribonacci numbers, etc.

https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers