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A174286 Number of distinct resistances that can be produced using at most n equal resistors (n or fewer 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 five resistors. 13
0, 0, 0, 0, 1, 3, 19, 67 (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

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: 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. 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.

CROSSREFS

A048211, A153588, A174283, A174284, A174285, A174286.

A176499, A176500, A176501, A176502 [From Sameen Ahmed Khan, Apr 27 2010]

Sequence in context: A249994 A178747 A071245 * A091968 A158714 A064056

Adjacent sequences:  A174283 A174284 A174285 * A174287 A174288 A174289

KEYWORD

more,nonn

AUTHOR

Sameen Ahmed Khan, Mar 15 2010

STATUS

approved

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Last modified May 23 16:37 EDT 2017. Contains 286925 sequences.