Fibonacci, a famous Italian mathematician, found such a set of numbers when studying rabbit breeding: 1, 1, 2, 3, 5, 8, 13, …, in which each number is equal to the sum of its first two numbers from the third number. Now, use each number in the set as the side length value of the square to construct the following square:

Then take 2, 3, 4, 5 … squares from left to right to form the following rectangles, which are denoted as ①, ②, ③, ④, …. The perimeters of the corresponding rectangles are shown in the following table:

Serial number 12344 ...

Circumference 6 10 x y …

Look at the chart carefully. X= in the above table.

16

，y=

26

.

If you continue to make a rectangle according to this rule, the circumference of the rectangle with serial number 8 is

178

This series was discovered as early as 12 century. At that time, it was only expressed by recursive formula, that is, the latter term was equal to the sum of the first two terms, and its general term formula was not given until18th century:

The nth number an = (1/√ 5) * {[(1+√ 5)/2] n-[(1-√ 5)/2] n}

Although the formula is a bit annoying, it is correct. You can try it if you don't believe me.

As for the solution, from now on, there are many difference equations and diagonalization of matrices. ...

The landlord can discuss the specific solution again.