Half-remembered integer sequences

[mtbc]

One show I miss from the television of my childhood is the Open University's lectures for distance learners. I have a hazy memory of an interesting sequence of increasing positive integers where it looked as if it was going to be one thing and it turned out to be another. I vaguely recall that for the first six numbers or so the sequence looked arithmetically obvious, like powers of two, but was in fact something else arising from geometry.

Somebody on a helpful online community managed to offer a good hypothesis for what I was trying to remember: from The On-Line Encyclopedia of Integer Sequences we have sequence A000127: Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes.

I ought to get around to finding myself some free online streaming that replaces those televised lectures that I welcomed.