Looking for a pseudo random number generation algorithm with specific properties

I'm looking for a pseudo random number generator which has the following properties:

• Non-repeating: The returned numbers must be unique until all numbers from 0 to n have been returned once, only then it can repeat each number once more, etc.
• Deterministic: If I used the same seed twice it needs to result in the same sequence.
• Few allocations: It should not require to allocate a large memory area in order to then mix its data up like sequence permutations would.

My goal is that I could initialize the random number generator with some seed value and then continuously call its function to generate the next number in the sequence, possibly passing it the previous one.