My armstrong furnace lately will run, cool down, shut down & immediately turn back on.
Will do this 2 or 3 times and then finally stay off. Seems to do it only during 1st program of the day & then is fine for the rest of the day.
I have noticed at times I do not here the thermostat 'click' for shutdown when it acts up. Thermostat??

Or one of those electronic safety features screwing up, like a airflow sensor, or fan motor sensor, ignition switch, or any of a number of do hickeys on your furnace. They only way to tell is with a skilled tech. Someone that knows how to check stuff and the tools to check stuff with, and most important, know what to check.

Could be as simple as a dirty filter or possibly a collapsed cold air return duct, I've seen both of them cause the symptom you describe. The fan off control is overheated by low air flow. When it finally cools down, it resets.

When I say immediately turns back on, it'll fire up again, run, cool down and shut off repeatedly 2 or 3 times. I wasn't clear about that.

I had an instance where the filter was dirty and cool down and then fire back up again without shutting down. This isn't that.