Schroeder Numbers List

Computes the first \e n values of the Schroeder sequence.

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Interface
Schroeder Numbers List
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Interface

C++

Schroeder Numbers List

std::vector<int>schroeder_numbers_list( int n )

This function generates an array with the first n values in the Schroeder sequence, given by the following recurrent formula

$S(n) = \frac{1}{n} ( (6n - 9) S(n-1) - (n-3)S(n-2) )$

(2)

with initial values

$S(1) = S(2) = 1$

(3)

The Schroeder sequence is also defined by

$S(n) = \frac{P(n)(3) - 3P(n-1)(3)}{4(n-1)}$

(4)

where $\inline P(n)(X)$ is the Legendre polynomial of order $\inline n$ .

Example:

#include <codecogs/maths/combinatorics/sequences/schroeder_numbers_list.h>
#include <iostream>
int main() {
  std::vector<int> result = Maths::Combinatorics::Sequences::schroeder_numbers_list(10);
  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: 10
1  1  3  11  45  197  903  4279  20793  103049

References:

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

Returns

an array of the first n values in the Schroeder sequence

Authors

Lucian Bentea (August 2005)

Source Code

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