I have forgotten

• https://me.yahoo.com
COST (GBP)
0.19
0.00
0

# Catalan Numbers List

Computes the Catalan numbers, of order 0 to n.
Controller: CodeCogs

C++

## Catalan Numbers List

 std::vectorcatalan_numbers_list( int n )
The formula for calculating the Catalan number of order n has several forms:



This function uses the following recurrence relation:


The Catalan number C(n) counts:

1) the number of binary trees with  vertices;

2) the number of ordered trees with  vertices;

3) the number of full binary trees with  vertices;

4) the number of well formed sequences of  parentheses;

5) the number of ways  ballots can be counted, in order, with n positive and n negative, so that the running sum is never negative;

6) the number of standard tableaus in a 2 by n rectangular <em> Ferrers </em> diagram;

7) the number of monotone functions  which satisfy , for all 

8) the number of ways to triangulate a polygon with  vertices.

### Example 1

#include <codecogs/maths/combinatorics/sequences/catalan_numbers_list.h>
#include <iostream>
int main() {
std::vector<int> result = Maths::Combinatorics::Sequences::catalan_numbers_list(8);
std::cout << "Number of values: " << result.size() << std::endl;
for (int i = 0; i < result.size(); i++)
std::cout << result[i] << "  ";
std::cout << std::endl;
return 0;
}
Output:
Number of values: 9
1  1  2  5  14  42  132  429  1430

## References:

SUBSET, a C++ library of combinatorial routines, http://www.csit.fsu.edu/~burkardt/cpp_src/subset/subset.html

### Returns

the Catalan numbers of order 0 to n

### Authors

Lucian Bentea (August 2005)
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.