#include long double f(long double p, long double pp) { return (19 * p - 12 * pp) / 4; } int main() { long double memo[128] = {}; memo[0] = 4; memo[1] = 3; // for(int i = 2; i <= 100; ++i) { // printf("%3d : %.20lf\n", i, (double)(memo[i] = f(memo[i-1], memo[i-2]))); // } long double diff[128]; // diff[i] = ax[i] - 4 * ax[i-1] => ax[i] = diff[i] + 4 * ax[i-1] diff[1] = -13; for(int i = 2; i < 128; ++i) { diff[i] = diff[i-1] * 3 / 4; } // for(int i = 1; i <= 100; ++i) { // printf("%lf %lf\n", (double)(memo[i] - 4 * memo[i-1]), (double)diff[i]); // } for(int i = 2; i < 128; ++i) { memo[i] = diff[i] + 4 * memo[i-1]; } for(int i = 2; i < 128; ++i) { memo[i] = memo[i-1] * 3 / 4; } // for(int i = 2; i <= 100; ++i) { // printf("%3d : %.20lf\n", i, (double)(memo[i])); // } int n; scanf("%d", &n); printf("%.30lf\n", (double)memo[n]); return 0; }