usage - Why is 間{かん} used to denote some amounts of time but not others?

I've been thinking about how to express a duration of time and how in the past I have added 間{かん} in situations where I found that I shouldn't have.

Take the following sentences as examples.

○：　３０分後ご飯を食べる。

☓：　３０分間後ご飯を食べる

○：　３年前日本に行った。

☓：　３年間前日本に行った。

○：　３時間後出かける。

☓：　３時後出かける。

Of course there are other examples that I could give but I think this kind of boils it down to the main point. When I think of 間 as a concept I generally think of it as an emphasis on start-to-finish time, like １年間日本語コース or something like that. Why, then, does this not apply to expressing time in the future/past? Specifically I have said before something like １年間後日本に行く or something like that, using 年間 in the same way that you would use 時間, only later to find that is not natural usage.

So this leads to the question of why these words cannot all be used in a consistent way. Is there something special about 時間 as a word that excuses it from counter, or are the rules inconsistent, or is there a pattern that I'm missing? I'm aware of 時間 as the word for hours, but as in Chocolate's answer, we don't say 一時間間.

Answer

Yes, [一分間]{いっぷんかん}, [一ヶ月間]{いっかげつかん} and [一年間]{いちねんかん} exist, but the [間]{かん} in them is not the same as in [一時間]{いちじかん} and [一週間]{いっしゅうかん}.

The 間 in 一時間 and 一週間 is a part of the counter words for "hour" and "week", but the counter words for "minute", "month" and "year" are 分, ヶ月 and 年 (not 分間, ヵ月間, 年間), and the 間 in 一分間, 一ヶ月間 and 一年間 is more like "for~~" or "during~~". So I think this is why you can say [一時間後]{いちじかんご} and [一週間後]{いっしゅうかんご} but not [一年間後]{いちねんかんご} or [一分間後]{いっぷんかんご}.

You can say [一週間]{いっしゅうかん}の[間]{あいだ}, [一時間]{いちじかん}の[間]{あいだ}, but [一分間]{いっぷんかん}の[間]{あいだ}, [一ヶ月間]{いっかげつかん}の[間]{あいだ} and [一年間]{いちねんかん}の[間]{あいだ} would be grammatically redundant, although quite a lot of people use ~~分間の間, ~~年間の間.

Don't ask me why we don't say [一週間間]{いっしゅうかんかん} for "for one week" or [一時間間]{いちじかんかん} for "for one hour" while we say [一分間]{いっぷんかん} (for one minute), [一ヶ月間]{いっかげつかん} (for one month), and [一年間]{いちねんかん} (for one year). (^_^;)