EPISODE · Aug 4, 2025 · 4 MIN
OEIS A000297: Triangles in Turán graphs and related combinatorial interpretations
from Intellectually Curious · host Mike Breault
Join us as we unpack OEIS A000297. The entry centers on the algebraic formula A_n = ((n+1)(n+3)(n+8))/6, which produces the initial terms 0, 4, 12, 25, 44, and, intriguingly, counts concrete combinatorial objects. For n > 3, A_n is the number of triangles in the Turán graph T_n, and the sequence also appears in other counting contexts that involve specific subset configurations of an n-element set. The OEIS page provides a generating function, typically listed as a rational form like 2x^2/(1−x)^4, plus ready-to-run code in Maple, Mathematica, and Python to generate terms. This entry exemplifies how a simple polynomial encodes rich combinatorial structure and how the OEIS serves as a hub linking algebra, counting problems, and computation.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.Sponsored by Embersilk LLC
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Join us as we unpack OEIS A000297. The entry centers on the algebraic formula A_n = ((n+1)(n+3)(n+8))/6, which produces the initial terms 0, 4, 12, 25, 44, and, intriguingly, counts concrete combinatorial objects. For n > 3, A_n is the number of triangles in the Turán graph T_n, and the sequence also appears in other counting contexts that involve specific subset configurations of an n-element set. The OEIS page provides a generating function, typically listed as a rational form like 2x^2/...
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OEIS A000297: Triangles in Turán graphs and related combinatorial interpretations
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