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.io.*;
import java.util.*;
//import java.math.*;
//import java.awt.Point;
 
public class Main {
	//static final long MOD = 998244353L;
	//static final long INF = -1000000000000000007L;
	static final long MOD = 1000000007L;
	//static final int INF = 1000000007;
	
	
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		PrintWriter pw = new PrintWriter(System.out);
		int N = sc.ni();
		long[][][][] dp = new long[N][4][4][4]; //A=0,G=1,C=2,T=3
		for (int n1 = 0; n1 < 4; n1++) {
			for (int n2 = 0; n2 < 4; n2++) {
				for (int n3 = 0; n3 < 4; n3++) {
					dp[2][n1][n2][n3] = 1;
				}
			}
		}
		dp[2][0][1][2] = 0;
		dp[2][0][2][1] = 0;
		dp[2][1][0][2] = 0;
		for (int i = 3; i < N; i++) {
			for (int a = 0; a < 4; a++) {
				for (int b = 0; b < 4; b++) {
					for (int c = 0; c < 4; c++) {
						for (int d = 0; d < 4; d++) {
							if (!(a==0&&b==1&&c==2)&&!(b==0&&c==1&&d==2)&&!(b==0&&a==1&&c==2)&&!(a==0&&c==1&&d==2)&&!(a==0&&c==1&&b==2)&&!(c==0&&b==1&&d==2)&&!(a==0&&b==1&&d==2)&&!(b==0&&d==1&&c==2)) {
								//this is a valid transition
								dp[i][b][c][d] += dp[i-1][a][b][c];
								dp[i][b][c][d] %= MOD;
							}
						}
					}
				}
			}
		}
		long ans = 0;
		for (int a = 0; a < 4; a++) {
			for (int b = 0; b < 4; b++) {
				for (int c = 0; c < 4; c++) {
					ans += dp[N-1][a][b][c];
				}
			}
		}
		ans %= MOD;
		pw.println(ans);
		pw.close();
	}
	
	static class SegmentTree {

		public long[][] ranges;

		public SegmentTree(long[] array) {
			ranges = new long[4*array.length+1][4];
			for (int i = 0; i < array.length; i++) {
				add(1,1,array.length,i+1,i+1,array[i]);
			}
		}

		//range update nums[updateL..updateR] += val;
		public void add(int n, int L, int R, int updateL, int updateR, long val) {
			push(n,L,R);
			if (updateL <= L && R <= updateR) {
				//fully contained
				ranges[n][3] += val;
				push(n,L,R);
				return;
			} else if (L>updateR || R<updateL || L==R) {
				//not contained at all or leaf
				return;
			}
			add(2*n,L,(L+R)/2,updateL,updateR,val); 
			add(2*n+1,(L+R)/2+1,R,updateL,updateR,val);
			ranges[n][1] = Math.min(ranges[2*n][1],ranges[2*n+1][1]);
			ranges[n][2] = Math.max(ranges[2*n][2],ranges[2*n+1][2]);
			ranges[n][0] = ranges[2*n][0] + ranges[2*n+1][0];
		}

		public long minQuery(int n, int L, int R, int Lq, int Rq) {
			push(n,L,R);
			if (Lq <= L && R <= Rq) {
				return ranges[n][1];
			} else if (R < Lq || Rq < L || L==R) {
				return 1000000000000007L;
			} else {
				return Math.min(minQuery(2*n,L,(L+R)/2,Lq,Rq),minQuery(2*n+1,(L+R)/2+1,R,Lq,Rq));
			}
		}

		public long maxQuery(int n, int L, int R, int Lq, int Rq) {
			push(n,L,R);
			if (Lq <= L && R <= Rq) {
				return ranges[n][2];
			} else if (R < Lq || Rq < L || L==R) {
				return -1L;
			} else {
				return Math.max(maxQuery(2*n,L,(L+R)/2,Lq,Rq),maxQuery(2*n+1,(L+R)/2+1,R,Lq,Rq));
			}
		}

		public long sumQuery(int n, int L, int R, int Lq, int Rq) {
			push(n,L,R);
			if (Lq <= L && R <= Rq) {
				return ranges[n][0];
			} else if (R < Lq || Rq < L || L==R) {
				return 0L;
			} else {
				return (sumQuery(2*n,L,(L+R)/2,Lq,Rq) + sumQuery(2*n+1,(L+R)/2+1,R,Lq,Rq));
			}
		}

		public void push(int n, int L, int R) {
			ranges[n][1] += ranges[n][3];
			ranges[n][2] += ranges[n][3];
			ranges[n][0] += (R-L+1)*ranges[n][3];

			if (L < R) {
				ranges[2*n][3] += ranges[n][3];
				ranges[2*n+1][3] += ranges[n][3];
			}

			ranges[n][3] = 0;
		}
	}
	
	public static long dist(long[] p1, long[] p2) {
		return (Math.abs(p2[0]-p1[0])+Math.abs(p2[1]-p1[1]));
	}
	
	//Find the GCD of two numbers
	public static long gcd(long a, long b) {
		if (a < b) return gcd(b,a);
		if (b == 0)
			return a;
		else
			return gcd(b,a%b);
	}
	
	//Fast exponentiation (x^y mod m)
	public static long power(long x, long y, long m) { 
		long ans = 1;
		x %= m;
		while (y > 0) { 
			if(y % 2 == 1) 
				ans = (ans * x) % m; 
			y /= 2;  
			x = (x * x) % m;
		} 
		return ans; 
	}
	
	public static int[][] shuffle(int[][] array) {
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		return array;
	}
	
    public static int[][] sort(int[][] array) {
    	//Sort an array (immune to quicksort TLE)
 
		Arrays.sort(array, new Comparator<int[]>() {
			  @Override
        	  public int compare(int[] arr1, int[] arr2) {
				  return arr1[1]-arr2[1]; //ascending order
	          }
		});
		return array;
	}
    
    public static long[][] sort(long[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    long[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<long[]>() {
			  @Override
        	  public int compare(long[] arr1, long[] arr2) {
				  //return 0;
				  if (arr1[0] < arr2[0]) {
					  return -1;
				  } else if (arr1[0] > arr2[0]) {
					  return 1;
				  } else {
					  return 0;
				  }
	          }
		});
		return array;
	}
    
    static class FastScanner { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner() { 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next() { 
            while (st == null || !st.hasMoreElements()) { 
                try { 
                    st = new StringTokenizer(br.readLine());
                } catch (IOException  e) { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int ni() { 
            return Integer.parseInt(next()); 
        } 
  
        long nl() { 
            return Long.parseLong(next()); 
        } 
  
        double nd() { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() { 
            String str = ""; 
            try { 
                str = br.readLine(); 
            } catch (IOException e) {
                e.printStackTrace(); 
            } 
            return str;
        }
    }
}