An occultist will ultimately know (up to) 49 spells.
The relevant part of the Implements section states (emphasis mine):
At 1st level, an occultist learns to use two implement schools. At 2nd level and every 4 occultist levels thereafter, the occultist learns to use one additional implement school, to a maximum of seven schools at 18th level. Each implement school adds one spell per spell level of that school of magic to the occultist’s spell list.
The relevant part of the Spell Casting section states (emphasis mine):
The occultist’s selection of spells is limited. For each implement school he learns to use, he can add one spell of each level he can cast to his list of spells known, chosen from that school’s spell list. If he selects the same implement school multiple times, he adds one spell of each level from that school’s list for each time he has selected that school.
When the occultist learns to cast a new level of spells, he immediately adds one spell of that level to his list of spells known from each implement school he knows (plus any extra spells from schools he has selected multiple times).
An occultist knows 1 spell per spell level per implement school; if they select the same implement school multiple times, it counts as multiple schools for the purposes of gaining spells (that is, if they select 3 different abjuration implements, then they receive 3 abjuration spells per spell level).
An occultist ultimately selects seven different implements, and gains access to seven different spell levels (0th-6th). Seven implements times seven spell levels equals forty-nine spells known. Note that this assumes there are sufficient spells available in the occultist's chosen school(s) that none of their choices are wasted; an occultist who chooses all seven of their implements from the illusion school, for example, will have less than seven choices for their 0th, 4th, 5th, and 6th-level spells.
Bards, summoners, and other 2/3-casters generally cap out at only 40 spells known (six each for 0th-4th, five each for 5th-6th). On the other hand, these classes don't have to worry about wasted choices due to overlapping schools the way the occultist does.