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Python BasicsMedium
F(N)th term recursion problem
Learn how to solve the 'F(N)th term recursion problem' problem. This detailed resource details brute force and optimized approaches.
Problem Statement
Medium
Write a function fnth_term(n) that computes the nth term of the sequence defined by: F(1) = 1, F(2) = 1, F(3) = 1, and for n > 3: F(n) = F(n-1) + F(n-2) + F(n-3). This is the Tribonacci sequence. The function takes a positive integer n and returns the nth term.
Constraints
- •1 <= n <= 30
Examples
Example 1
Input
n = 5
Output
5
Explanation
F(1)=1, F(2)=1, F(3)=1, F(4)=1+1+1=3, F(5)=3+1+1=5.
Example 2
Input
n = 4
Output
3
Explanation
F(4) = F(3) + F(2) + F(1) = 1 + 1 + 1 = 3.
Example 3
Input
n = 7
Output
17
Explanation
F(5)=5, F(6)=3+5+1? Let's trace: F(4)=3, F(5)=5, F(6)=F(5)+F(4)+F(3)=5+3+1=9, F(7)=F(6)+F(5)+F(4)=9+5+3=17.
Need a Hint?
Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.
Edge Cases to Watch
- Empty list or null input variables
- Single item lists/arrays
- Extremely large input bounds causing integer or stack overflow
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