OEIS A000112: Even sequences with period 2N

In this episode we dive into A000112, the OEIS entry counting even (mirror-symmetric) sequences with period 2N. We explain what “even” means in this setting—sequences whose one period reads the same forward and backward around its midpoint—and how these fit inside the larger family of 2N-periodic sequences. We’ll explore how A000112 connects to A000013 and A000208, including the key recurrence A(2N) + A(N) = 2·A000208(2N+1), and discuss a straightforward asymptotic view for large N. We’ll look at the first terms (1, 2, 4, 8, 20, 56) to see the growth, and point to the symmetry-type literature (Gilbert & Riordan) and Sloan’s handbook for deeper exploration. A compact tour of the combinatorial ideas behind the numbers and the rich web of connections in the OEIS is on the docket for today.

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