790. Domino and Tromino Tiling

We have two types of tiles: a 2x1 domino shape, and an "L" tromino shape. These shapes may be rotated.

XX  <- domino

XX  <- "L" tromino
X

Given N, how many ways are there to tile a 2 x N board? Return your answer modulo 10^9 + 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.)

**Example:**
Input: 3
Output: 5
Explanation:
The five different ways are listed below, different letters indicates different tiles:
XYZ XXZ XYY XXY XYY
XYZ YYZ XZZ XYY XXY

Note:

• N will be in range [1, 1000].

# @lc code=start
using LeetCode

function num_tilings(N::Int)
    f0, f1= 1, 1
    g0, g1 = 0, 1
    for i in 1:N-1
        f0, f1, g0, g1 = f1, f0 + f1 + 2 * g0, g1, g1 + f1
    end
    f1
end
# @lc code=end

num_tilings (generic function with 1 method)

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