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A174284 Number of distinct resistances that can be produced using at most n equal resistors (n or fewer resistors) in series, parallel and/or bridge configurations. 12
1, 3, 7, 15, 35, 79, 193, 489 (list; graph; refs; listen; history; text; internal format)



This sequence is a modification of A153588, which uses only series and parallel combinations. Since a bridge circuit requires minimum of five resistances the first four terms coincide. The fifth term also coincides, since set corresponding to five resistors for the bridge give {1}, is already obtained in the fourth set corresponding to the fourth term in A153588.


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

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).


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.


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

Sequence in context: A221945 A077946 A077970 * A182892 A124696 A081669

Adjacent sequences:  A174281 A174282 A174283 * A174285 A174286 A174287




Sameen Ahmed Khan, Mar 15 2010



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Last modified March 18 11:49 EDT 2018. Contains 300749 sequences. (Running on oeis4.)