As I recall, triple butted was marketed as a better alternative to double butted frames in the 1970s. I recall that seamless, triple butted steel frames by Reynolds were considered to be the best and I think Peugeot made a few.
This is a 1983 Austro-Daimler with a triple butted Reynolds 531 frame:
Source: 1983 Austro-Daimler | Cycle Logical
Am I "misremembering" as another member has suggested?