OEIS A000306: Unlabeled trees with diameter 8

Today on Deep Dive we explore OEIS sequence A000306—the count of unlabeled, connected acyclic graphs (trees) whose diameter is exactly 8. We unpack what diameter means in graph terms and why counting such trees is surprisingly hard even with a simple definition. We’ll trace the historical arc—from Sloan’s 1973 handbook to the OEIS inclusion in 1995 (with identifiers like M3552 and 1440)—and note early work by Johnny Olum on diameter and height. We also discuss modern computation, including Christian Severs’ PRI program (May 2023) that extended calculations to thousands of terms, and what the offset 9-2 means for the starting point. Finally, we’ll reflect on the growth of the sequence (1, 4, 19, 66, 219, …) and ponder future questions in diameter-restricted trees and other graph properties.

Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.

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