TopCoder problem "TriangleCount" used in SRM 199 (Division I Level One , Division II Level Two)



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

0)
    
2
Returns: 5
There are four small triangles and one big triangle.
1)
    
4
Returns: 27
This is the example from the problem statement.
2)
    
100
Returns: 256275

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=2889

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=5074&pm=2889

Writer:

legakis

Testers:

lbackstrom , brett1479

Problem categories:

Math