OEIS A00011C: Symmetry in the Even Terms of Periodic Sequences

Join us for a deep dive into A00011C, the elegant bisection of the periodic-sequence world formed by the even terms of A000011. We unpack how this symmetry emerges, guided by Gilbert and Reordan’s classification, and illustrate it with concrete terms like 3, 1, 2, 4, 8, 18, 44, 122. We’ll explore how the central anchors around powers of two reveal a deliberate mirrored structure and discuss how the exponential growth ties to longer periods. Placing A00011C in the broader OEIS landscape, we’ll touch on potential connections to coding theory and combinatorial design, all while keeping the focus on the beauty of symmetry in sequences. If you’re a number theory student, this is a tour of how order and pattern arise from a simple bisection.

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