The Diamond Lattice

This comprehensive pedagogical guide provides an in-depth exploration of the Lichtenberg sequence (OEIS A000975) with extensive teaching support for independent learners. Every section includes detailed teaching boxes with prerequisites and learning objectives, numerous worked examples with step-by-step calculations, intuition boxes explaining the mathematics, extensive practice problems with complete solutions, warnings about common errors, historical context, and real-world applications. We use ONLY the mathematically correct sum rule definition a(n) = 2n−1−a(n−1) and explicitly document incorrect formulations found in some literature. The guide proves key properties including ratio convergence to 2 with exponentially decaying error (∼ 3/4 n), presents the novel Diamond Lattice geometric characterization, analyzes binary representations, establishes the 50% duty cycle theorem, and explores connections to computer science and combinatorics. Suitable for motivated high school students through undergraduate mathematics majors.

Total length: approximately 40 pages with appendicesCopyright@DavidCoates