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A232005
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Number of distinct resistances that can be produced from a circuit of resistors with resistances 1, 2, ..., n using only series and parallel combinations.
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0
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OFFSET
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1,2
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COMMENTS
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Found by exhaustive search: all configurations of resistors were enumerated, resistances calculated, sorted, and distinct values counted.
This sequence allows any circuits to be combined in series or in parallel (akin A000084); A051045 requires circuits to be combined with a single resistor at a time.
This sequence regards circuits as distinct only if their resistance is different; A006351 regards circuits distinct if their configuration is different, although some may have the same resistance.
This sequence considers resistors with contiguous resistances 1, 2, ..., n; A005840 considers arbitrarily different resistors, while A048211 considers n equal resistances.
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LINKS
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EXAMPLE
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a(2) = 2 since given a 1-ohm and a 2-ohm resistor, a series circuit yields 3 ohms, while a parallel circuit yields 2/3 ohms, which thus yields two distinct resistances.
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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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STATUS
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approved
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