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A174285
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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.
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13
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0, 0, 0, 0, 1, 3, 17, 61, 235, 815, 2563, 7585, 22277, 62065, 169489, 452621, 1191617
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,6
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LINKS
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EXAMPLE
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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.
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MAPLE
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See link section: A174285(n) = nops(SetA174285(n)).
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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From Stampfli's paper, a(8) corrected and a(9)-a(12) added by Eric M. Schmidt, Sep 09 2017
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STATUS
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approved
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