AOJ 0168 Kannondou http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0168 漸化式が問題文に書いてあるのでそれをメモ化して取り出すだけ。

AOJ_0168.cpp

#include <iostream>
#include <vector>

#define REP(i, n) for ( int i = 0; i < n; i++ )

using namespace std;

int main() {
    int n;
    
    vector<int> open(30);
    open[0] = 1;
    open[1] = 2;
    open[2] = 4;

    for ( int i = 3; i < 30; i++ ) {
        open[i] = open[i-1] + open[i-2] + open[i-3];
        // cout << i << ":" << open[i] << endl;
    }

    while(cin >>n, n) {
        n -= 1; // 添字に合わせる

        cout << (open[n]/10/365)+1 << endl;
    }
    
    return 0;
}