I am reading Uri Alon's "Intro to Systems Biology" where he introduces the concept of subgraphs in networks. He claims that with 3 nodes, you can make 13 subgraphs, with 4 nodes 199 subgraphs, and with 5 nodes 9364 subgraphs.
I have tried coming up with a formula for number of subgraphs given n nodes, and have scoured the internet but still have not found an answer. Any help is appreciated.
The numbers are tabulated at https://oeis.org/A003085 but no closed-form formula is given, which is strong evidence that no closed-form formula is known, which may mean that no closed-form formula exists.