Problem 364: Comfortable distance

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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.

Let T(N) be the number of possibilities that N seats are occupied by N people with the given rules. 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.