Problem Statement
Given an equilateral triangle with side length N divided into a triangular grid of triangles with side length 1, count the total number of triangles present in the grid. For example, if N is 4:
/\
/__\
/\ /\
/__\/__\
/\ /\ /\
/__\/__\/__\
/\ /\ /\ /\
/__\/__\/__\/__\
Here there are ten right-side-up and six up-side-down triangles with a side length of 1, six right-side-up and one up-side-down triangles with a side length of 2, three right-side-up triangles with a side length of 3, and one right-side-up triangle with a side length of 4. The total number of triangles is 27.
Definition
- Class:
- TriangleCount
- Method:
- count
- Parameters:
- int
- Returns:
- int
- Method signature:
- int count(int N)
- (be sure your method is public)
Constraints
- N will be between 1 and 500, inclusive.
Examples
2
Returns: 5
There are four small triangles and one big triangle.
3
Returns: 13
4
Returns: 27
This is the example from the problem statement.
5
Returns: 48
100
Returns: 256275
1
Returns: 1
500
Returns: 31406375
6
Returns: 78
7
Returns: 118
8
Returns: 170
9
Returns: 235
10
Returns: 315
15
Returns: 988
20
Returns: 2255
25
Returns: 4303
50
Returns: 32825
200
Returns: 2025050
300
Returns: 6806325
400
Returns: 16100100
450
Returns: 22907925
499
Returns: 31218625
500
Returns: 31406375
100
Returns: 256275
1
Returns: 1
97
Returns: 234073
499
Returns: 31218625
3
Returns: 13