Every Tuesday, the feds publish allocation data for the next week here: https://www.hhs.gov/coronavirus/covid-19-vaccines/distribution/index.html
That leads to Friday, when the state publishes allocation data for the next week here: https://www.dshs.state.tx.us/coronavirus/immunize/vaccineallocations.aspx
The feds have a table just for J&J (Janssen) and the state breaks it out in their weekly allocations. So you can see how much J&J is coming to Texas and where it is going by the weekend before the distribution week.
I don't have a link for the J&J ramp but I have read articles saying that the first week was a dump of all of the vaccine they had made up until that point, in the time when they were waiting for their trial to be over and for EUA approval. That was "Week 13". Now we are in a period where the initial dump is distributed and they are just distributing what they are able to manufacture that week, which is lower. However, I have read that once the factory ramp period is over they are going to be producing a lot of J&J quickly ... and that period could be over around the end of March.
Put that together and we had a happy J&J week 13, followed by a trickle for a few weeks, followed hopefully by a flood in April.