The sum of the squares of consecutive Fibonacci numbers is another Fibonacci number. Specifically we have

and so we have the following right triangle.

The sum of the squares of consecutive Fibonacci numbers is another Fibonacci number. Specifically we have

and so we have the following right triangle.

It looks like the only Pythagorean triple of this sort is (0,1;1).

https://math.stackexchange.com/questions/1012999/square-fibonacci-numbers

What does F2n+1 the hypotenuese notation mean?

Nah itâ€™s observed by all combinations.

0^2 + 1^2 = 1

1^2 + 1^2 = 2

1^2 + 2^2 = 5

2^2 + 3^2 = 13

…

You always get the odd-numbered numbers in the Fibonacci sequence.

The subscripts are the index of the Fibonacci numbers, so F_n is the nth Fibonacci number.