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A174285 Number of distinct resistances that can be produced using n equal resistors in series and/or parallel, confined to the five arms (four arms and the diagonal) of a bridge configuration. Since the bridge requires a minimum of five resistors, the first four terms are zero. 13

%I

%S 0,0,0,0,1,3,17,61,235,815,2563,7587

%N Number of distinct resistances that can be produced using n equal resistors in series and/or parallel, confined to the five arms (four arms and the diagonal) of a bridge configuration. Since the bridge requires a minimum of five resistors, the first four terms are zero.

%H Sameen Ahmed Khan, <a href="http://arxiv.org/abs/1004.3346/">The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel</a>, arXiv:1004.3346v1 [physics.gen-ph], (20 April 2010).

%H Antoni Amengual, <a href="http://dx.doi.org/10.1119/1.19396">The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel</a>, American Journal of Physics, 68(2), 175-179 (February 2000). Digital Object Identifier (DOI): 10.1119/1.19396

%H Marx Stampfli, <a href="https://dx.doi.org/10.1016%2Fj.amc.2016.12.030">Bridged graphs, circuits and Fibonacci numbers</a>, Applied Mathematics and Computation, Volume 302, 1 June 2017, Pages 68-79.

%e Example 1: Five equal unit resistors. Each arm of the bridge has one unit resistor, leading to an equivalent resistance of 1; so the set is {1} and its order is 1. Example 2: Six equal unit resistors. Four arms have one unit resistor each and the fifth arm has two unit resistors. Two resistors in the same arm, when combined in series and parallel result in 2 and 1/2 respectively (corresponding to 2: {1/2, 2} in A048211). The set {1/2, 2}, in the diagonal results in {1}. Set {1/2, 2} in any of the four arms results in {11/13, 13/11}. Consequently, with six equal resistors, we have the set {11/13, 1, 13/11}, whose order is 3.

%Y Cf. A048211, A153588, A174283, A174284, A174285, A174286, A176499, A176500, A176501, A176502.

%K more,nonn,changed

%O 1,6

%A _Sameen Ahmed Khan_, Mar 15 2010

%E From Stampfli's paper, a(8) corrected and a(9)-a(12) added by _Eric M. Schmidt_, Sep 09 2017

%E Name edited by _Eric M. Schmidt_, Sep 09 2017

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Last modified September 21 15:34 EDT 2017. Contains 292312 sequences.