/* 
 * Calculate 
 *
 *    x[n] = (13/3)*x[n-1] - (4/3)*x[n-2], x[0] = 1, x[1] = 1/3
 *
 * To compile: 
 *
 *      make recur1
 *
 *    or
 *
 *      gcc -O0 recur1.c -o recur1
 *
 *    or
 *
 *      clang -O0 recur1.c -o recur1
 */

#include <stdio.h>
#include <math.h>

#define N 30

int main(void)
{
    double x[N];
    int i;
    x[0] = 1.;
    x[1] = 1./3.;

    for (i = 2; i < N; i++)
    {
        x[i] = 13./3. * x[i - 1] - 4./3. * x[i - 2];
        printf("%3d   % 14.10f    %14.10e\n", i, x[i], pow(1./3., i));
    }

    return 0;
}