# Domino and Tromino

You have two types of tiles: a `2 x 1` domino shape and a tromino shape. You may rotate these shapes.

![](https://assets.leetcode.com/uploads/2021/07/15/lc-domino.jpg)

Given an integer n, return *the number of ways to tile an* `2 x n` *board*. Since the answer may be very large, return it **modulo** `109 + 7`.

In a tiling, every square must be covered by a tile. Two tilings are different if and only if there are two 4-directionally adjacent cells on the board such that exactly one of the tilings has both squares occupied by a tile.

![](https://assets.leetcode.com/uploads/2021/07/15/lc-domino1.jpg)

```
Input: n = 3
Output: 5
Explanation: The five different ways are show above.
```

## Idea

{% hint style="info" %}
Dynamic Programming + Pattern finding
{% endhint %}

![](https://718974022-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FSuJgG7D29QwYhL3TYnjr%2Fuploads%2FKRb90wlLhXSjRRTBeOU5%2FIMG_6BF4677D1CCC-1.jpeg?alt=media\&token=bb0adc8d-0c66-4b05-8d02-3ea6f06a9e5c)

## Code

```java
public int numTilings(int n) {
        if(n==1){
            return 1;
        }
        if(n==2){
            return 2;
        }
        int mod = (int)(Math.pow(10,9)+7);
        
        int[] dp = new int[n+1];
        dp[0] = 1;
        dp[1] = 1;
        dp[2] = 2;
        
        for(int i=3;i<=n;i++){
            dp[i] = ((2*dp[i-1])%mod)+dp[i-3];
            dp[i] %= mod;
        }
        
        return dp[n];
    }
```


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