Ternary Strings Avoiding 00
combinatorics kmp matrix-exponentiation
Count the strings of length N over the alphabet {0, 1, 2} that do NOT contain 00 as a contiguous substring, modulo 109+7.
Input: one integer N.
Output: the count mod 109+7.
Constraints:
- 1 ≤ N ≤ 1018
Sample Tests
Input 1
2
Output 1
8
Input 2
3
Output 2
22
Input 3
1
Output 3
3
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