I am not a very knowledgeable person nor am I a very good philosopher. However, I am able to think logically. Based on given information, one can conclude certain things or speculate different aspects. When one is faced with limited knowledge/information, the most logical thing to do is to extrapolate the existing data to match possible results. Please note that this will not ensure that the conclusions are correct; this just gives you a range of possibilities that are more likely to be correct than other answers. Unexpected answers to simple questions may not be common, yet they do exist.
Furthermore, when generally stating something as drastic as "when given limited information the simplest solution that matches that information is most likely correct", you must back your point up with proof. In certain situations, your statement may prove to be correct however, in many cases, the integrity/truth of such a statement can be questioned. A very important principle in philosophy that must be noted is that the lack of knowledge does not justify the truth of another. For example, one cannot argue to prove the existence of God by saying: "Well, since we don't know how the first atom was created, then God must have created it." One must approach such argument from a different direction.
Back to your question specifically about the sequence, I see your logic behind what you deem to be the pattern/algorithm of the sequence and I agree because I do not see other possibilities. Although I may be completely wrong, It seems to me that the simplest answer (in this case) will most likely be correct. However, this is case sensitive and in relation to other situations, this theory may not necessarily hold true.