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.

0, 0, 0, 0, 1, 3, 17, 61, 235, 815, 2563, 7585, 22277, 62065, 169489, 452621, 1191617

Offset

1,6

Links

Table of n, a(n) for n=1..17.

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): 10.1119/1.19396

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).

Rainer Rosenthal, Maple programs SetA174285 and SetA174286

Marx Stampfli, Bridged graphs, circuits and Fibonacci numbers, Applied Mathematics and Computation, Volume 302, 1 June 2017, Pages 68-79.

Index to sequences related to resistances.

Example

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.
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.

Maple

See link section: A174285(n) = nops(SetA174285(n)).

Crossrefs

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

Sequence in context: A168547 A208996 A273949 * A227427 A120386 A061982

Adjacent sequences: A174282 A174283 A174284 * A174286 A174287 A174288

Keyword

nonn,more

Author

Sameen Ahmed Khan, Mar 15 2010

Extensions

From Stampfli's paper, a(8) corrected and a(9)-a(12) added by Eric M. Schmidt, Sep 09 2017

Name edited by Eric M. Schmidt, Sep 09 2017

a(13)-a(17) added by Rainer Rosenthal, Feb 04 2021

a(12) corrected by Marx Stampfli, Nov 04 2022

Status

approved