CountLatticePoint | Topcoder Archive

Problem Statement

Consider a two dimensional plane.

Given an int N, return the number of lattice points whose Manhattan distance from (0, 0) is strictly less than N (including the point (0, 0).)

Here's the example for small cases. The center point in each case is (0, 0).

                                .
                      .        ...
            .        ...      .....
  .        ...      .....    .......
            .        ...      .....
                      .        ...
                                .

N = 1     N = 2     N = 3     N = 4

Definition

Class:: CountLatticePoint
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 100, inclusive.

Examples

```
1
```
```
Returns: 1
```
Described in problem statement.
```
2
```
```
Returns: 5
```
```
3
```
```
Returns: 13
```
```
4
```
```
Returns: 25
```
```
95
```
```
Returns: 17861
```

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