Some type combos never make it because they are unbalanced or make no since at all. Ludicolo makes sense because of lilipads. A Fire/Grass would be difficult to come up with. Now, a Fire/Bug type would be easier to comeby.
To see what a Fire/Grass type would be like:
Resistance - Electric/x0.5 Grass/x0.25 Steel/x0.5
Weakness - Flying/x2 Poison/x2 Rock/x2
Everything else would be normal damage.
Fire/Water:
Resistance - Fire/x0.25 Ice/x0.25 Bug/x0.5 Steel/x0.25
Weakness - Electric/x2 Ground/x2 Rock/x2
Everything else would be normal damage.
I really, really want a Dark/Fighting type.
Resistance - Psychic/x0 Rock/x0.5 Dark/x0.25 Ghost/x0.5
Weakness - Fighting/x2 Flying/x2
Everything else would deal normal damage.
Dark/Psychic:
Resistance - Psychic/x0
Weakness - Bug/x4
Everything else would deal normal damage.