> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# N-th Tribonacci Number Python Solution

> Tested Python solution for LeetCode 1137 with 17 pytest cases. Generate a practice environment with lcpy.

LeetCode 1137, Easy. Topics: Math, Dynamic Programming, Memoization. [View on LeetCode](https://leetcode.com/problems/n-th-tribonacci-number/description/).

Generate this problem as a practice environment: tested reference solution, 17 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 1137   # by problem number
lcpy gen -s n_th_tribonacci_number   # by problem name
```

## Problem

The Tribonacci sequence Tn is defined as follows:

T0 = 0, T1 = 1, T2 = 1, and Tn+3 = Tn + Tn+1 + Tn+2 for n >= 0.

Given `n`, return the value of Tn.

### Examples

```
Input: n = 4
Output: 4
Explanation:
T_3 = 0 + 1 + 1 = 2
T_4 = 1 + 1 + 2 = 4
```

```
Input: n = 25
Output: 1389537
```

### Constraints

* `0 <= n <= 37`
* The answer is guaranteed to fit within a 32-bit integer, ie. `answer <= 2^31 - 1`.

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/n_th_tribonacci_number/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/n_th_tribonacci_number/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(n)
    # Space: O(1)
    def tribonacci(self, n: int) -> int:
        if n == 0:
            return 0
        if n == 1 or n == 2:
            return 1

        t0, t1, t2 = 0, 1, 1
        for _ in range(3, n + 1):
            t0, t1, t2 = t1, t2, t0 + t1 + t2
        return t2
```

## Complexity

| Time | Space |
| ---- | ----- |
| O(n) | O(1)  |

## Tags

[NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode).