Statistical methods for Sequence learning I am bit more traditional and I am looking for a statistical method that can help me also do inference or predictions.

I have some table that contains some transitions, where each row of the table correspond to a specific user. If you are into python this is it:

smallData=pd.DataFrame(np.array([[1,2,3,4,5],[4,5,6,7,8],[1,2,3,3,3],[1,2,2,3,3],[1,2,3,5,3]]),columns=range(0,5))
smallData
Out[266]: 
   0  1  2  3  4
0  1  2  3  4  5
1  4  5  6  7  8
2  1  2  3  3  3
3  1  2  2  3  3
4  1  2  3  5  3


Now first row means that the following transitions happen
1-2-3-4-5

this kind of transitions can be of course be visualized as a tree or diagram. So far I have not found any method or library in python or R that can calculate the statistics of transitions. For example for the two transitions [1,2] three transition can happen


Transition 3 by 50%, 
Transition 4 by 25% and 
Transition 5 by 25%. 


These were calculated from the table above.

Even harder will be to predict two steps forward.

I have seen the topic of sequence prediction to be discussed a lot in the machine learning community by using LSTM. I still wonder if in the statistics community are methods to handle such problems and if yes if there are in python, R libraries that can be used for such problem.
it sounds like a stochastic process problem. Have you looked into estimating transition matrices for markov chains?