Twice Equation large numbers Linear Recursive

Topic links: https://nanti.jisuanke.com/t/A1541

Question is intended: to give you a L, L is not less than the minimum demand of N, so that there is a positive integer m satisfying the 2m (m + 1) = n (n + 1)

Analysis: This idea is no problem to see it simply (n + 1) directly from the playing table 2m (m + 1) = n, Law came to be found in front of a few is 3,20,119,696,4059

Try to find the law, if he will not find on the direct use of Linear Recurrence factor formula to violence enumerate successfully obtain recurrence formula is f (n) = 6f (n-1) -f (n-2) + 2;

import java.io.*;
import java.util.*;
import java.math.*;

public class Main {
    public static void main(String args[]) {
        Scanner cin = new Scanner(System.in);
        int T=cin.nextInt();
        BigInteger[] fn=new BigInteger [1500];
        BigInteger two=new BigInteger("2");
        BigInteger six=new BigInteger("6");
        BigInteger L;
        fn[1]=new BigInteger("3");fn[2]=new BigInteger("20");
        for(int i=3;i<=1200;i++) {
            fn[i]=fn[i-1].multiply(six).subtract(fn[i-2]).add(two);
        }
        for(int i=0;i<T;i++) {
            L=cin.nextBigInteger();
            for(int j=1;j<=1200;j++) {
                if(L.compareTo(fn[j])<=0) {
                    System.out.println(fn[j]);
                    break;
                }
            }
        }
    }
}