This is an interesting question, so I am going to try to calculate it using Serebii's and Bulbapedia's databases along with my own experience. Also note that for this I'm assuming one of each remake, and also one of either Black or White and of Black 2 or White 2.
Step 1: Start with the total number of Pokémon, 802
Step 2: Subtract all the mythical Pokémon. So that's Mew, Celebi, Jirachi, Manaphy, Shaymin, Arceus, Victini, Keldeo, Genesect, Meloetta, Diancie, Hoopa, Volcanion, Magearna, & Marshadow. Deoxys is not included because he can be captured legitimately in ORAS now. Thus 802 - 15 = 787
Step 3: Subtract all the trade-evolutions that cannot be obtained without trading. That's Slwoking, Kingdra, Scizor, Porygon2, Porygon-Z, Huntail, Gorebyss, Rhyperior, Electivire, Magmortar, Dusknoir, Conkeldurr, Escavalier, Accelgor, Aromatisse, Slurpuff, and Gourgeist. The following are not included because there are in-game methods of obtaining them:
-Alakazam(NPC trade in B2W2)
-Machamp(NPC trade in Yellow)
-Gengar(SOS battles in SuMo)
-Golem(NPC trade in SuMo)
-Steelix(found wild in Gen IV games)
-Politoed(SOS battles in SuMo)
-Milotic(alternate evolution method)
-Gigalith(NPC trade in B2W2)
-Trevenant(found wild in Gen VI games)
So that's 787 - 17 = 770
Step 4: Check version exclusives(since you said one game per generation). For this I'm assuming you're getting Platinum(for all three cover legends of Gen IV), a combination of either HeartGold and Silver or SoulSilver and Gold(in addition to AlphaSapphire going with SoulSilver and OmegaRuby going with HeartGold), and a combination of either Black and White 2 or White and Black 2. In which case you're only dealing with 5 version exclusives each in Gens VI and VII. So that's 770 - 10 = 760. Adjust if you're getting specific games that don't comply with my conditions.
You can also deduct numbers for starters or fossils, but you should be able to obtain most of them from restarting games and/or various postgame events in HGSS, ORAS, and SuMo. So my final number is 760. ^_^
