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How many subsets of a (2n+1)-element set have n elements or less?

To figure this out I started by using a workable example. Obviously n must be small to keep the total number of subsets small. So I started with n=1 and so there are 8 total subsets. And of course in general there will be 2^(2n+1) subsets. Writing these subsets out in order from smallest to largest seems to reveal a pattern. There is 1 empty set, 2n+1 one element sets and 2n 2 element sets all the way up to 1 2n+1 element set. So there must be 2n+1-n element sets with n elements or less plus the empty set to give me n+2. Does this sound correct?

Thanks