Output prediction from a sequence of data Given the machine learning libraries available for many different languages, it's possible to utilise algorithms where you don't need to have a detailed understanding of their application or workings or datascience in general.

I have tried to find a list of algorithms that are suitable for sequence prediction from a window of previous input values, which I could then apply in such a library e.g. Accord for C# but have failed.

Each observation I have is an array of 2-dimensonal data in the following form: {MODE1/2/3, int 1-98}. That is, multiple inputs produce multiple outputs. I'd like to examine preceding sets of values from either t-1 or t-x where x could be a variable amount of preceding value sets.

So, I'd like to ask what algorithms excel at prediction from a window of sequence data, and what are their strengths / weaknesses.
Have a look on conditional random field. Conditional random fields  are a probabilistic framework for labeling and segmenting structured data, such as sequences, trees and lattices. The underlying idea is that of defining a conditional probability distribution over label sequences given a particular observation sequence, rather than a joint distribution over both label and observation sequences. The primary advantage of CRFs is their conditional nature, resulting in the relaxation of the independence assumptions. Additionally, CRFs avoid the label bias problem. It is often used for labeling or parsing of sequential data.