Problem 364

Comfortable distance

There are `N` seats in a row. `N` people come after each other to fill the seats according to the following rules:

- If there is any seat whose adjacent seat(s) are not occupied take such a seat.
- If there is no such seat and there is any seat for which only one adjacent seat is occupied take such a seat.
- Otherwise take one of the remaining available seats.

The following figure shows T(4)=8.

We can verify that T(10) = 61632 and T(1 000) mod 100 000 007 = 47255094.

Find T(1 000 000) mod 100 000 007.

**
These problems are part of
Project Euler
and are licensed under
CC BY-NC-SA 2.0 UK
**