TriangleCount | Topcoder Archive

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.
```
4
```
```
Returns: 27
```
This is the example from the problem statement.
```
100
```
```
Returns: 256275
```

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