FIELDDiagrams | Topcoder Archive

Problem Statement

A Ferrers diagram of the partition of positive number n = a₁ + a₂ + ... + a_k, for a list a₁, a₂, ..., a_k of k positive integers with a₁ ≥ a₂ ≥ ... ≥ a_k is an arrangement of n boxes in k rows, such that the boxes are left-justified, the first row is of length a₁, the second row is of length a₂, and so on, with the kth row of length a_k. Let's call a FIELD diagram of order fieldOrder a Ferrers diagram with a₁ ≤ fieldOrder, a₂ ≤ fieldOrder - 1, ..., a_k ≤ fieldOrder - k + 1, so a FIELD diagram can have a number of rows which is less than or equal to fieldOrder. Your method will be given fieldOrder, it should return the total number of FIELD diagrams of order fieldOrder.

Definition

Class:: FIELDDiagrams
Method:: countDiagrams
Parameters:: int
Returns:: long
Method signature:: long countDiagrams(int fieldOrder)
(be sure your method is public)

Constraints

fieldOrder will be between 1 and 30, inclusive

Examples

```
2
```
```
Returns: 4
```
There are four possible FIELD diagrams for fieldOrder equal to 2, corresponding to partitions: (1), (2), (1, 1), (2,1). They are shown in the picture below. There white stands for unused space in a row and red for boxes, corresponding to FIELD diagrams.
```
3
```
```
Returns: 13
```
```
5
```
```
Returns: 131
```

This problem statement is the exclusive and proprietary property of Topcoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of Topcoder, Inc. is strictly prohibited. (c)2024, Topcoder, Inc. All rights reserved.