

A174283


Number of distinct resistances that can be produced using n equal resistors in, series, parallel and/or bridge configurations.


20



1, 2, 4, 9, 23, 57, 151, 415, 1157, 3191, 8687, 23199, 61677, 163257, 432541, 1146671, 3039829
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

This sequence is a variation on A048211, which uses only series and parallel combinations. Since a bridge circuit requires minimum of five resistances the first four terms coincide. For the definition of "bridge" see A337516.


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), 175179 (February 2000).
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.genph], (20 April 2010).
Sameen Ahmed Khan, Farey sequences and resistor networks, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 153162.
Sameen Ahmed Khan, Beginning to Count the Number of Equivalent Resistances, Indian Journal of Science and Technology, Vol. 9, Issue 44, pp. 17, 2016.
Hugo Pfoertner, Increase of number of representable resistances by allowing bridges, Plot2 of a(n)/A048211.


EXAMPLE

Example 1: Five 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. Thus a(5) = A048211(5) + 1 = 23.
Example 2: Six unit resistors: a bridge with 6 resistors yields A174285(6) = 3 different resistances and the series parallel combinations give A048211(6) = 53 resistances, but resistance 1 is counted twice. The union of the forementioned resistances has cardinality 53+31 = 55. There are two more circuits to be considered: the bridge with five unit resistors and the sixth unit resistor either in parallel (value 1/2) or in series (value 2). Both values 1/2 and 2 are not counted by A048211(6) or A174285(6), so the total is 55 + 2 = 57.  Rainer Rosenthal, Oct 25 2020


CROSSREFS

Cf. A048211, A153588, A174284, A174285, A174286, A176499, A176500, A176501, A176502, A180414, A337516, A337517.
Sequence in context: A159330 A159331 A135346 * A337516 A340920 A337517
Adjacent sequences: A174280 A174281 A174282 * A174284 A174285 A174286


KEYWORD

nonn,hard,nice,more


AUTHOR

Sameen Ahmed Khan, Mar 15 2010


EXTENSIONS

a(8) corrected and a(9)a(17) from Rainer Rosenthal, Oct 29 2020


STATUS

approved



