Number Theorey?, Pure Math?, Charles Babbage

GIVEN: At Charles Babbage’s Wedding (fictional) the tables are labeled ‘A’ to ‘Z’. Each of the center pieces is an arrangement of golden spheres.

These golden spheres are arranged on the tables as follows:

babbage_golden_balls

FIND: How many golden spheres are there on Table ‘F’? How about on Table ‘P’?