OEIS A00098: Two-kind partitions of N

Explore A00098, the number of ways to partition n when each part size 1, 2, and 3 comes in two distinct kinds. We’ll walk through small examples (A3 = 10) and show how this sequence connects to partitions of odd numbers into three odd parts, including a convolution view with A00041 and A01399. We’ll also look at the main formulas: the generating function, a recursive formula, and an asymptotic expression that reveals its growth, highlighting why this simple counting setup leads to rich structure.

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