*See:
www.geeksforgeeks.org/program-for-nth-fibonacci-number/*

The Fibonacci numbers are integers in the following sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .

In mathematical terms, the Fibonacci numbers are defined by the relationship

`F`_{n} = F_{n-1} + F_{n-2}

with seed values
`F`

and _{0} = 0`F`

_{1} = 1

Write a program that calculates Fibonacci numbers. Run the program and display the numbers (max number 100).

Display the number of the Fibonacci numbers generated.

Write a program that calculates numbers defined by the relationship

```
(X
```_{n})^{2} = (X_{n-1})^{2} + (X_{n-2})^{2}

Run the program and display the numbers (max number 500).

with seed values
`X`

and _{0} = 0`X`

.
_{1} = 1

Display the number of the Fibonacci numbers generated.

Write a program that

- asks the user for seed values
- ask the user for the max number
- displays numbers using the relationship
`X`

_{n}= X_{n-1}+ X_{n-2} - Display a count of the numbers found

Write a program that calculates the reverse Fibonacci numbers. Run the program and display the numbers (max number + or - 100).

`F`_{n-2} = F_{n} - F_{n-1}

with seed values
`F`

and _{0} = 0`F`

_{1} = 1

*Note: the same sequences of numbers is generated
but but with alternating signs.*

Write a program that calculates Lucas numbers. Run the program and display the numbers (max number 100).

`L`_{n} = L_{n-1} + L_{n-2}

with seed values
`L`

and _{0} = 2`L`

_{1} = 1

Write a program that calculates the reverse Lucas numbers. Run the program and display the numbers (max number + or - 100).