## Palindrome-containing strings

### Problem 486

Let F_{5}(`n`) be the number of strings `s` such that:

`s`consists only of '0's and '1's,`s`has length at most`n`, and`s`contains a palindromic substring of length at least 5.

For example, F_{5}(4) = 0, F_{5}(5) = 8,
F_{5}(6) = 42 and F_{5}(11) = 3844.

Let D(`L`) be the number of integers `n` such that
5 ≤ `n` ≤ `L` and F_{5}(`n`) is divisible by 87654321.

For example, D(10^{7}) = 0 and D(5·10^{9}) = 51.

Find D(10^{18}).