Semitotalistic

Those are fully symmetric, but not semitotalistic; the main difference lies, among other things, in whether a pair of diametrically opposed live cells should give birth to a new cell.

Source: wiktionary

Bays looked at several spots in the paramerization space of 'semi-totalistic' ('semi-totalistic' that my new state is a function of only my own state and the sum of my neighbors' states) on cubic as well as 'half-cubic' lattices.

Source: wiktionary

I've recently discovered four new semi-totalistic rules (i.e. defined by neighbor counts, like Life) that have self-replicating patterns in them.

Source: wiktionary