Number of Locks

A factory makes spring locks. Each lock has $n$ slots ($1 < n < 17$, $n$ is a natural number), and the height of every slot is one of 1, 2, 3, 4. Ignore units.

A lock ships only when it meets both conditions below.

• At least one pair of neighboring slots has a height difference of exactly 3.
• The slots use at least 3 different height values.

Over every way to assign the 4 height values to the $n$ slots, find how many locks meet both conditions.

Each line holds one value $n$, the number of slots. The last line holds -1, which marks the end of the input.

For each input value, print the number of locks on its own line. Begin the line with the input value $n$, then a colon and a space, then the counted number of locks, so every line has the form n: count.