Binary Strings Avoiding 111
combinatorics matrix-exponentiation
Count the binary strings of length N with no three consecutive 1s, modulo 109+7.
Input: one integer N.
Output: the count modulo 109+7.
Constraints:
- 1 ≤ N ≤ 1018
Sample Tests
Input 1
1
Output 1
2
Input 2
2
Output 2
4
Input 3
3
Output 3
7
Input 4
4
Output 4
13
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