Lens sequences

A family of sequences produced by a non-homogeneous linear recurrence formula derived from the geometry of circles inscribed in lenses is introduced and studied. Mysterious ``underground’’ sequences underlying them are discovered in this paper.

💡 Research Summary

The paper introduces a novel family of integer sequences that arise from the geometry of circles inscribed in a planar lens – the region formed by two intersecting circles. By applying the Descartes circle theorem to the chain of mutually tangent circles inside the lens, the authors derive a non‑homogeneous second‑order linear recurrence
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