OEIS A000097: Partitions with two colors of 1s and 2s

We dive into A000097, counting partitions of n when each 1 and 2 comes in two colors. We'll trace its rich set of interpretations—from Euler transforms and generating functions to recurrences, near-identical partition pairs, and distance-graph connections—showing how a simple counting rule unlocks a web of math in the OEIS.

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