OEIS A000200: Number of bicentered hydrocarbons with N atoms

In this episode we explore OEIS A000200, the sequence that counts bicentered hydrocarbons with N carbon atoms. We explain bicentered meaning two shared carbon atoms (bridgeheads) in a two-ring system, distinguishing fused and bridged bicyclic skeletons while excluding spiro structures. We'll show how the bicyclo[a.b.c] naming encodes three carbon bridges between the bridgeheads and how the total N counts both bridgeheads and bridge carbons. Then we connect chemistry to math: counting distinct skeletal isomers is a graph-enumeration problem with rich links to combinatorics, generating functions, and polycyclic chemistry. We’ll illustrate small-N examples, discuss methods and known results, and point you to the OEIS entry for formulas, references, and further connections to chemistry and graph theory.

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