In this Deep Dive we explore OEIS A000217, the triangular numbers T_n = n(n+1)/2. We trace their roots from the early geometry of the Pythagoreans to Gauss, and survey the many ways they appear in counting, geometry, and algebra. We’ll highlight core identities like T_n + T_{n+1} = (n+1)^2, plus a suite of combinatorial interpretations (handshakes, domino sets, etc.). We’ll also peek at generating functions and some deeper connections, including links to even perfect numbers via Mersenne primes.

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

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