We count non-isomorphic trees with diameter exactly 6. Starting at seven vertices, the sequence shows how many distinct trees exist for n vertices, with terms that grow rapidly as you add vertices. The OEIS page reveals history (formerly M2887N1158, N1158) and the offset 7,2, plus how terms are generated via generating-function techniques like the shifted Euler transform and Piri code. It also connects to Riordan’s foundational work on counting trees by height and diameter, offers cross-references to related diameter sequences, and notes ongoing computation (Seavers, Irvine) that keeps OEIS a living resource.
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