OFFSET
1,6
LINKS
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.
EXAMPLE
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. Union of the previous terms is {1} and the union with these three is again {11/13, 1, 13/11}. So the terms for five and six resistors are 1 and 3 respectively.
MAPLE
See link section: A174286(n) = nops(SetA174286(n)).
CROSSREFS
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 05 2021
STATUS
approved