ROS wheel odometry is based on the linear and angular velocity(s) of the platform. You just need to find those values for your 3 wheeled car. For 2 wheeled, the calculations are very simple. I assume if you've made a 3 wheel car then you have some complex controller which you're already feeding that into.
You just need to publish those values in the message with an appropriate covariance and you should be on your way.
Odometry is not directly just encoder ticks, its the speed and / or pose of the robot given the ticks.
Could you link the stack/package you are looking at?
Is this what you're looking for?
Actually I'm looking for how to acquire odometer data from motor encoders. I need to know what exactly I have to publish from encoders.