Hosoya's Triangle

The Fibonacci triangle or Hosoya's triangle is a triangular arrangement of numbers based on Fibonacci numbers. Each number is the sum of two numbers above in either the left diagonal or the right diagonal. The first few rows are: 
 

👁 Hosoya's Triangle

The numbers in this triangle follow the recurrence relations 
 

👁 recurrence relations 1

Relation to Fibonacci numbers 
The entries in the triangle satisfy the identity 
 

👁 recurrence relations 2

Thus, the two outermost diagonals are the Fibonacci numbers, while the numbers on the middle vertical lines are the squares of the Fibonacci numbers. All the other numbers in the triangle are the product of two distinct Fibonacci numbers greater than 1. The row sums are the first convolved Fibonacci numbers.
Sources: Stackoverflow, Wikipedia
Given a positive integers n. The task is print Hosoya's triangle of size n. 
Examples: 

Input : n = 4
Output :
1
1 1
2 1 2
3 2 2 3

Input : n = 5
Output :
1
1 1
2 1 2
3 2 2 3
5 3 4 3 5

Below is the implementation of printing Hosoya's triangle of height n: 

Output:  

1 
1 1 
2 1 2 
3 2 2 3 
5 3 4 3 5 

Time Complexity: O(n²)

Auxiliary Space: O(n²)
Below is the implementation of printing Hosoya's triangle of height n using Dynamic Programming: 

Output:  

1 
1 1 
2 1 2 
3 2 2 3 
5 3 4 3 5 

Time complexity: O(n*n)

space complexity: O(n*n)