Journal of Integer Sequences, Vol. 23 (2020), Article 20.8.5

Ellipse Chains and Associated Sequences


Hacène Belbachir and Soumeya Merwa Tebtoub
Department of Mathematics
USTHB, RECITS Laboratory
P. O. Box 32
El Alia 16111
Bab Ezzouar
Algiers
Algeria

László Németh
Institute of Mathematics
University of Sopron
Bajcsy Zs. u. 4
Sopron H9400
Hungary
and
USTHB, RECITS Laboratory
Algeria

Abstract:

We define circle and ellipse chains tangent to the branches of a hyperbola and the terms of the chains are mutually tangent to each other. Our goal is to derive recurrence relations for the parameters of chains elements and to establish some connections between integer sequences and chains.

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(Concerned with sequences A001075 A001078 A001079 A001109 A001352 A001541 A001542 A001906 A002878 A003499 A003500 A004190 A004291 A004292 A004294 A004298 A005248 A005319 A005320 A011922 A023039 A025169 A049660 A049670 A052530 A054890 A057076 A060645 A064170 A075848 A076218 A078986 A078987 A081554 A084070 A087215 A087799 A097316 A097725 A097836 A097839 A097844 A098706 A099370 A099857 A106328 A106329 A111282 A122652 A122653 A134492 A201157 A202299 A207832 A231896 A239364 A273182 A276598 A276602.)

Received April 8 2020; revised versions received August 27 2020; September 10 2020. Published in Journal of Integer Sequences, September 11 2020.

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