Signal timetable count

Count the legal timetables of a single railway track for one day, and the freight trains they contain.

A single-track section is watched minute by minute. A timetable for a day of minutes minutes assigns every minute either to idle (.) or to a train; a train always occupies consecutive minutes, and every minute of the day belongs to exactly one thing. There are three kinds of train:

• a local (LL) occupies 2 minutes and has no restrictions;
• an express (XXX) occupies 3 minutes and must be followed by at least one idle minute, unless it finishes at the last minute of the day;
• a freight (FFF) occupies 3 minutes and must be preceded by at least two idle minutes. The start of the day counts as idle time, so a freight may start in the first minute (nothing before it) or in the second minute (after one idle minute).

Two timetables are different if some minute differs. Trains may follow each other directly whenever the rules above allow it, and a train may not be cut off by the end of the day.

For example, with 3 minutes there are 5 timetables: ..., LL., .LL, XXX and FFF.

Input: minutes, an integer.

Output: a list [timetables, freight_trains]: the number of legal timetables, and the total number of freight trains over all of those timetables (a timetable with two freights contributes 2), each taken modulo 1000000007.