OEIS A000309: Rooted Planar Bridgeless Cubic Maps with Two Gen Nodes

In this episode we unpack A000309, the sequence 1, 1, 4, 24, 176, 1456 that counts rooted planar bridgeless cubic maps with two gen nodes. We’ll also see how the same numbers count rooted planar, non-separable triangulations with 3n edges (and with 2n triangles), and for description trees of type 2-man-2 with n edges. We’ll explore the surprising connections to Tamari lattices and lambda calculus, inspired by Noam Zeldberger’s 2018 talk linking planar maps, Tamari lattices, and lambda calculus. Finally, we’ll discuss how these combinatorial motifs surface in architecture and what they reveal about the underlying unity of discrete structures and the simple formulas that generate the sequence.

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