OEIS A000264: Three-edge-connected rooted cubic maps with two E-nodes and a distinguished Hamiltonian cycle

In this episode, we dive into A000264, which counts three-edge-connected rooted cubic maps with two E-nodes and a distinguished Hamiltonian cycle. We’ll unpack what a cubic map is, what it means for it to be 3-edge-connected, and why a distinguished Hamiltonian cycle is a central piece of the combinatorial puzzle. From there, we’ll sketch how mathematicians approach enumeration in such structured graphs, discuss the role of Hamiltonian cycles in these objects, and connect these ideas to broader themes in graph theory and the theory of integer sequences in the OEIS.

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