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A174283 Number of distinct resistances that can be produced using n equal resistors in, series, parallel and/or bridge configurations. 13
1, 2, 4, 9, 23, 57, 151, 409 (list; graph; refs; listen; history; text; internal format)



This sequence is a modification of the Sequence A048211, which uses only series and parallel combinations. Since a bridge circuit requires minimum of five resistances the first four terms coincide.


Antoni Amengual, The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel, American Journal of Physics, 68(2), 175-179 (February 2000). Digital Object Identifier (DOI): http://dx.doi.org/10.1119/1.19396 [From Sameen Ahmed Khan, Apr 27 2010]

S. A. Khan, Farey sequences and resistor networks, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 153-162.

Sameen Ahmed Khan, Beginning to count the number of equivalent resistances, Indian Journal of Science and Technology, 2016, Vol 9(44), DOI: 10.17485/ijst/2016/v9i44/88086, http://www.indjst.org/index.php/indjst/article/viewFile/88086/75398


Table of n, a(n) for n=1..8.

Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, arXiv:1004.3346v1 [physics.gen-ph], (20 April 2010).


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: 6 equal 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 6 equal resistors, we have the set {11/13, 1, 13/11}, whose order is 3.


A048211, A153588, A174283, A174284, A174285, A174286

A176499, A176500, A176501, A176502 [From Sameen Ahmed Khan, Apr 27 2010]

Sequence in context: A159330 A159331 A135346 * A268172 A151404 A027071

Adjacent sequences:  A174280 A174281 A174282 * A174284 A174285 A174286




Sameen Ahmed Khan, Mar 15 2010



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Last modified April 3 18:40 EDT 2020. Contains 333198 sequences. (Running on oeis4.)