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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 minimum of five resistors, the first four terms have been defined to be zero corresponding to 1, 2, 3 and four resistors. The sequence starts with 5 resistors. 12
0, 0, 0, 0, 1, 3, 17, 53 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,6

REFERENCES

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

LINKS

Table of n, a(n) for n=5..12.

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

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.

CROSSREFS

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

Sequence in context: A018691 A225727 A163943 * A093418 A173733 A258032

Adjacent sequences:  A174282 A174283 A174284 * A174286 A174287 A174288

KEYWORD

more,nonn

AUTHOR

Sameen Ahmed Khan, Mar 15 2010

STATUS

approved

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Last modified June 24 11:40 EDT 2017. Contains 288697 sequences.