Perrin_Numbers_List — Sequences

Computes the first \e n values of a Perrin sequence.

View versions (2)

Interface

#include <codecogs/maths/combinatorics/sequences/perrin_numbers_list.h>

using namespace Maths::Combinatorics::Sequences;

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

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

$$P(n+1) = P(n-1) + P(n-2)$$

(1)

with initial values

$$P(0) = 3 \qquad P(1) = 0 \qquad P(2) = 2$$

(2)

A special property of this sequence is that, if n is a prime then it must evenly divide $P(n)$.

Example 1

#include <codecogs/maths/combinatorics/sequences/perrin_numbers_list.h>
#include <iostream>
int main() {
  std::vector<int> result = Maths::Combinatorics::Sequences::perrin_numbers_list(11);
  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: 11
3  0  2  3  2  5  5  7  10  12  17

References

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

Parameters

the number of Perrin numbers to generate

Returns

the first n Perrin numbers, of orders 0 through n - 1