A slightly more versatile way to define a rule table is to separate the central cell from its neighbors, treating their sum according to the state of the central cell. Life is a rule of this kind, because live cells evolve differently from the others, but in both cases the decision depends on how many of the remaining eight neighbors are present. The adjective describing these rules is semitotalistic.
The display for a semitotalistic rule would consist of two rows, one
for birth and one for survival, with a common header showing totals.
The number of neighborhoods with a common total and central cell would
be 
, for Moore neighborhoods.