How many ways are there to permute the integers from 1 to 1000 under the condition that two consecutive numbers must have different parity?
I know that there are two possible cases: either the sequence starts with an even or it is starts with an odd. Then the sequence alternates parity all the way through.
But I am not sure how to mathematically count the permutations of evens and permutations of odds. Like what formula do I use?