Neural Network Time Series Input

All, I am attempting to replicate the work done using Long Short Term Momory Artificial Neural Networks proposed in this thesis by following this (great) example. I have a given dataset for which I train the neural network (an interpolating function x[t] output from NDSolve): I train:

* Create a Neural Network and correctly format the training data to \
predict the above time series *)

inputdata = Flatten@Table[Evaluate[x[t] /. s], {t, 200, 5500}];
trainingdata =
RandomSample[
List /@ Most[#] -> List@Last[#] & /@ (Partition[inputdata, 51, 1])];
LSTMANN =
NetChain[{LongShortTermMemoryLayer, LinearLayer},
"Input" -> {50, 1}, "Output" -> 1]

trainedLSTMANN = NetTrain[LSTMANN, trainingdata]

Then I attempt to feed the data into the neural network. I want to give it 50 samples and have the ANN output one sample (the next predicted sample in time). I have been doing the following:

ListPlot[{Flatten@Table[Evaluate[x[t] /. s], {t, 200, 550}],
Flatten@NestList[Append[Rest[#], trainedLSTMANN[#]] &,
Table[Evaluate[x[t] /. s], {t, 0, 49}], 350][[All, -1]]},
Joined -> True, PlotLegends -> {"True Values", "Predicted Values"}]

But I think I know this is wrong. This is me sending the initial values of x[t] into the ANN input and the output is the same each time, no? And I repeat is 350 times? I want to send a number of samples into the ANN, output the predicted value, then repeat but in a windowed fashion where the next number of samples is time shifted. I am not extremely proficient in Mathematica and have been unable to fully understand the syntax here (what does [[All, -1]] contribute? I know that it is indexing a vector but am confused at the purpose).

Any help is appreciated!