Problem:
Score : 400 points

Problem Statement

You are given an integer N. Find the number of strings of length N that satisfy the following conditions, modulo 10^9+7:

The string does not contain characters other than A, C, G and T.

The string does not contain AGC as a substring.

The condition above cannot be violated by swapping two adjacent characters once.

Notes

A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.

For example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.

Constraints

3 \leq N \leq 100

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of strings of length N that satisfy the following conditions, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

61

There are 4^3 = 64 strings of length 3 that do not contain characters other than A, C, G and T. Among them, only AGC, ACG and GAC violate the condition, so the answer is 64 - 3 = 61.

Sample Input 2

4

Sample Output 2

230

Sample Input 3

100

Sample Output 3

388130742

Be sure to print the number of strings modulo 10^9+7.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    static final Scanner sc  = new Scanner(System.in);
    static final int MOD = (int) 1E9 + 7;
    static final int INF = Integer.MAX_VALUE;
    
    public static void main(String[] args) {
        int N = nint();
        final int A = 1, G = 2, C = 3, T = 4;
        final int[] cs = {A, G, C, T};
        
        int[][][][] dp = new int[N+1][5][5][5]; // [文字列の長さL][L-2文字目][L-1文字目][L文字目]
        dp[0][4][4][4] = 1;
        
        for (int n = 1; n <= N; n++) {
            for (int c3 : cs) {
                for (int c2 : cs) {
                    for (int c1 : cs) {
                        for (int cn : cs) {
                            if (           c2 == A && c1 == G && cn == C) continue;
                            if (           c2 == A && c1 == C && cn == G) continue;
                            if (           c2 == G && c1 == A && cn == C) continue;
                            if (c3 == A &&            c1 == G && cn == C) continue;
                            if (c3 == A && c2 == G            && cn == C) continue;
                            
                            dp[n][c2][c1][cn] += dp[n-1][c3][c2][c1];
                            dp[n][c2][c1][cn] %= MOD;
                        }
                    }
                }
            }
        }
        
        int ans = 0;
        for (int c3 : cs) {
            for (int c2 : cs) {
                for (int c1 : cs) {
                    ans += dp[N][c3][c2][c1];
                    ans %= MOD;
                }
            }
        }
        System.out.println(ans);
    }
    
    static long max(long... longs) {
        return Arrays.stream(longs).max().getAsLong();
    }
    
    static long min(long... longs) {
        return Arrays.stream(longs).min().getAsLong();
    }

    private static long nlong() {
        return sc.nextLong();
    }

    private static int nint() {
        return sc.nextInt();
    }

    private static String nstr() {
        return sc.next();
    }

    private static char[] nchars() {
        return sc.next().toCharArray();
    }

    private static char[] nchars(int padL, int padR) {
        char[] temp = sc.next().toCharArray();
        char[] ret = new char[temp.length + padL + padR];
        System.arraycopy(temp, 0, ret, padL, temp.length);
        return ret;
    }

    private static int[] nints(int n) {
        return nints(n, 0, 0);
    }

    private static int[] nints(int n, int padL, int padR) {
        int[] a = new int[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nint();
        return a;
    }

    private static long[] nlongs(int n) {
        return nlongs(n, 0, 0);
    }

    private static long[] nlongs(int n, int padL, int padR) {
        long[] a = new long[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nlong();
        return a;
    }
    
    private static double[] ndoubles(int n) {
        return ndoubles(n, 0, 0);
    }
    
    private static double[] ndoubles(int n, int padL, int padR) {
        double[] d = new double[n + padL + padR];
        for (int i = 0; i < n; i++) {
            d[padL + i] = sc.nextDouble();
        }
        return d;
    }

    private static char[][] nchars2(int h, int w) {
        return nchars2(h, w, 0);
    }

    private static char[][] nchars2(int h, int w, int pad) {
        char[][] a2 = new char[h + pad * 2][w + pad * 2];
        for (int i = 0; i < h; i++)
            System.arraycopy(nchars(), 0, a2[pad + i], pad, w);
        return a2;
    }
}