OEIS A000305: Number of Certain Rooted Planar Maps episode artwork

EPISODE · Aug 12, 2025 · 5 MIN

OEIS A000305: Number of Certain Rooted Planar Maps

from Intellectually Curious · host Mike Breault

In this episode we explore OEIS A000305, which counts rooted, non-separable planar maps with N edges. A planar map is a connected graph embedded in the plane without edge crossings; rooted means we designate a directed edge to fix a reference, and non-separable means removing any single vertex leaves the map connected. The sequence starts 1, 4, 18, 89, 466, … and has the elegant closed form A_N = 2·(3N−3)! / (N!·(2N−1)!). This result comes from Tutte’s pioneering generating-function approach, with Brown extending the study to related map classes. This is a classic example of how a concrete combinatorial counting problem yields a neat exact formula, a staple of the OEIS bridge between objects and numbers.Note:  This podcast was AI-generated, and sometimes AI can make mistakes.  Please double-check any critical information.Sponsored by Embersilk LLC

Episode metadata supplied by the publisher feed · Published Aug 12, 2025

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In this episode we explore OEIS A000305, which counts rooted, non-separable planar maps with N edges. A planar map is a connected graph embedded in the plane without edge crossings; rooted means we designate a directed edge to fix a reference, and non-separable means removing any single vertex leaves the map connected. The sequence starts 1, 4, 18, 89, 466, … and has the elegant closed form A_N = 2·(3N−3)! / (N!·(2N−1)!). This result comes from Tutte’s pioneering generating-function approach,...

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