Journal of Integer Sequences, Vol. 23 (2020), Article 20.11.6

Lens Sequences

Jerzy Kocik
Department of Mathematics
Southern Illinois University, Carbondale
Carbondale, IL 62901


We study a family of sequences produced by a non-homogeneous linear recurrence formula derived from the geometry of circles inscribed in lenses. The sequences lead to mysterious "underground" sequences underlying them. The results are consequences of the theorem on four disks in general configuration, a generalization of the celebrated Descartes theorem on circles.

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(Concerned with sequences A000032 A000045 A000079 A000217 A000466 A001519 A001654 A001834 A001835 A002878 A005013 A005246 A005247 A005408 A011900 A011922 A021913 A026741 A027941 A032908 A054318 A061278 A064170 A075269 A079935 A081078 A084158 A084159 A099025 A101265 A101879 A109437.)

Received June 18 2007; revised versions received September 17 2007; June 30 2020; October 19 2020. Published in Journal of Integer Sequences, December 5 2020.

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