OEIS A000028: Even binary sequences with period 2n

We explore A000028 from the OEIS: the number of equivalence classes of binary strings of length 2n that repeat with period 2n, where each period contains an even number of 1s. Two blocks are considered the same if you can cyclically rotate them (translate around the circle) or swap 0s and 1s (complement). We’ll unpack what 'even' means in this context, what 'period 2n' means, and why counting these patterns matters. We’ll walk through simple examples, discuss the kinds of formulas and references the OEIS entry provides, and connect these ideas to the broader notion of binary necklaces and symmetry.

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