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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
)

var mod = 1000000007
var inf = 1000000007

func main() {
	r := bufio.NewReader(os.Stdin)
	var n int
	fmt.Fscan(r, &n)

	var dp [101][5][5][5]int
	dp[0][0][0][0] = 1
	for len := 0; len < n; len++ {
		for i := 0; i < 5; i++ {
			for j := 0; j < 5; j++ {
				for k := 0; k < 5; k++ {
					for l := 1; l < 5; l++ {
						if i == 1 && k == 2 && l == 3 {
							continue
						}
						if i == 1 && j == 2 && l == 3 {
							continue
						}
						if j == 1 && k == 2 && l == 3 {
							continue
						}
						if j == 2 && k == 1 && l == 3 {
							continue
						}
						if j == 1 && k == 3 && l == 2 {
							continue
						}

						dp[len+1][j][k][l] += dp[len][i][j][k]
						dp[len+1][j][k][l] %= mod
					}
				}
			}
		}
	}

	ans := 0
	for i := 1; i < 5; i++ {
		for j := 1; j < 5; j++ {
			for k := 1; k < 5; k++ {
				ans += dp[n][i][j][k]
				ans %= mod
			}
		}
	}

	fmt.Println(ans)
}

// permutations
func permutations(arr []int) [][]int {
	var helper func([]int, int)
	res := [][]int{}

	helper = func(arr []int, n int) {
		if n == 1 {
			tmp := make([]int, len(arr))
			copy(tmp, arr)
			res = append(res, tmp)
		} else {
			for i := 0; i < n; i++ {
				helper(arr, n-1)
				if n%2 == 1 {
					tmp := arr[i]
					arr[i] = arr[n-1]
					arr[n-1] = tmp
				} else {
					tmp := arr[0]
					arr[0] = arr[n-1]
					arr[n-1] = tmp
				}
			}
		}
	}
	helper(arr, len(arr))
	return res
}

// Union-Find
type unionFind struct {
	d []int
}

func newUnionFind(n int) *unionFind {
	uf := new(unionFind)
	uf.d = make([]int, n)
	for i := 0; i < n; i++ {
		uf.d[i] = -1
	}
	return uf
}

func (uf *unionFind) find(x int) int {
	if uf.d[x] < 0 {
		return x
	}
	uf.d[x] = uf.find(uf.d[x])
	return uf.d[x]
}

func (uf *unionFind) unite(x, y int) bool {
	rootX := uf.find(x)
	rootY := uf.find(y)
	if rootX == rootY {
		return false
	}

	if uf.d[rootX] < uf.d[rootY] {
		uf.d[rootX] += uf.d[rootY]
		uf.d[rootY] = rootX
	} else {
		uf.d[rootY] += uf.d[rootX]
		uf.d[rootX] = rootY
	}

	return true
}

func (uf *unionFind) same(x, y int) bool {
	return uf.find(x) == uf.find(y)
}

func (uf *unionFind) size(x int) int {
	return -uf.d[uf.find(x)]
}

// mod
func modpow(a, n, mod int) int {
	res := 1
	for n > 0 {
		if n%2 != 0 {
			res = res * a % mod
		}
		a = a * a % mod
		n = n / 2
	}
	return res
}

func modinv(n, mod int) int {
	return modpow(n, mod-2, mod)
}

func modcomb(n, a, mod int) int {
	x := 1
	y := 1
	for i := 0; i < a; i++ {
		x = x * (n - i)
		x %= mod
		y = y * (i + 1)
		y %= mod
	}
	return x * modpow(y, mod-2, mod) % mod
}

func modfactorial(n, mod int) int {
	result := 1
	for i := 1; i <= n; i++ {
		result = (result * i) % mod
	}
	return result
}

// Combination ...
type Combination struct {
	facts, invs []int
	mod         int
}

// NewCombination ...
func NewCombination(n, mod int) Combination {
	return Combination{
		facts: make([]int, n+1),
		invs:  make([]int, n+1),
		mod:   mod,
	}
}

func (cmb *Combination) calc(n, k int) int {
	ret := cmb.facts[n] * cmb.invs[k]
	ret %= cmb.mod
	ret = ret * cmb.invs[n-k]
	ret %= cmb.mod
	return ret
}

func (cmb *Combination) init(n int) {
	cmb.facts[0] = 1
	// 階乗を算出
	for i := 1; i <= n; i++ {
		cmb.facts[i] = cmb.facts[i-1] * i % cmb.mod
	}
	// 逆元を算出
	cmb.invs[n] = modinv(cmb.facts[n], cmb.mod)
	for i := n - 1; i >= 0; i-- {
		cmb.invs[i] = cmb.invs[i+1] * (i + 1) % cmb.mod
	}
}

// Utility
func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}

func max(x, y int) int {
	if x > y {
		return x
	}
	return y
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func primeFactor(x int) map[int]int {
	res := make(map[int]int)
	for i := 2; i*i <= x; i++ {
		for x%i == 0 {
			res[i]++
			x = x / i
		}
	}
	if x != 1 {
		res[x] = 1
	}
	return res
}

func divisor(x int) []int {
	res := make([]int, 0)
	for i := 1; i*i <= x; i++ {
		if x%i == 0 {
			res = append(res, i)
			if i != x/i {
				res = append(res, x/i)
			}
		}
	}
	return res
}

func gcd(x, y int) int {
	if y == 0 {
		return x
	}
	return gcd(y, x%y)
}

func lcm(x, y int) int {
	return x / gcd(x, y) * y
}

func reverseString(s string) string {
	r := []rune(s)
	for i, j := 0, len(r)-1; i < len(r)/2; i, j = i+1, j-1 {
		r[i], r[j] = r[j], r[i]
	}
	return string(r)
}

func pow(a, n int) int {
	ret := 1
	for i := 1; i <= n; i++ {
		ret *= a
	}
	return ret
}

// Queue ...
type Queue []int

// pop ...
func (q *Queue) empty() bool {
	return len(*q) == 0
}

// push ...
func (q *Queue) push(i int) {
	*q = append(*q, i)
}

// pop ...
func (q *Queue) pop() (int, bool) {
	if q.empty() {
		return 0, false
	} else {
		res := (*q)[0]
		*q = (*q)[1:]
		return res, true
	}
}

// Stack ...
type Stack []int

// pop ...
func (s *Stack) empty() bool {
	return len(*s) == 0
}

// push ...
func (s *Stack) push(i int) {
	*s = append(*s, i)
}

// pop ...
func (s *Stack) pop() (int, bool) {
	if s.empty() {
		return 0, false
	} else {
		index := len(*s) - 1
		res := (*s)[index]
		*s = (*s)[:index]
		return res, true
	}
}

// priority_queue
type intHeap []int

func (h intHeap) Len() int           { return len(h) }
func (h intHeap) Less(i, j int) bool { return h[i] > h[j] }
func (h intHeap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }
func (h *intHeap) Push(x interface{}) {
	*h = append(*h, x.(int))
}
func (h *intHeap) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}

// sortable points
type point struct {
	x int
	y int
}

type points []point

func (p points) Len() int {
	return len(p)
}

func (p points) Less(i, j int) bool {
	return p[i].x < p[j].x
}

func (p points) Swap(i, j int) {
	p[i], p[j] = p[j], p[i]
}