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Problems > Tiling 2xN with Dominoes and L-Trominoes

Tiling 2xN with Dominoes and L-Trominoes

Difficulty: 1900 4000 ms 128 MB

combinatorics matrix-exponentiation

Count the tilings of a 2×N board using 2×1 dominoes AND L-shaped trominoes, modulo 109+7. The recurrence is f(N)=f(N−1)+f(N−2)+2g(N−1), g(N)=f(N−1)+g(N−1); track both.

Input: one integer N.

Output: the count modulo 109+7.

Constraints:

  • 1 ≤ N ≤ 1018

Sample Tests

Input 1
1
Output 1
1
Input 2
2
Output 2
4
Input 3
3
Output 3
9
Input 4
4
Output 4
25

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