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A174284
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Number of distinct finite resistances that can be produced using at most n equal resistors (n or fewer resistors) in series, parallel and/or bridge configurations.
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14
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0, 1, 3, 7, 15, 35, 79, 193, 493, 1299, 3429, 9049, 23699, 62271, 163997, 433433, 1147659, 3040899
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OFFSET
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0,3
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COMMENTS
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This sequence is a variation on A153588, which uses only series and parallel combinations. The circuits with exactly n unit resistors are counted by A174283, so this sequence counts the union of the sets, which are counted by A174283(k), k <= n. - Rainer Rosenthal, Oct 27 2020
For n = 0 the resistance is infinite, therefore the number of finite resistances is a(0) = 0. Sequence A180414 counts all resistances (including infinity) and so has A180414(0) = 1 and A180414(n) = a(n) + 1 for all n up to n = 7. For n > 7 the networks get more complex, producing more resistance values, so A180414(n) > a(n) + 1. - Rainer Rosenthal, Feb 13 2021
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LINKS
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FORMULA
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a(n) = #(union of all S(k), k <= n), where S(k) is the set which is counted by A174283(k). - Rainer Rosenthal, Oct 27 2020
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EXAMPLE
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Since a bridge circuit requires a minimum of five resistors, the first four terms coincide with A153588. The fifth term also coincides since the set corresponding to five resistors for the bridge, i.e. {1}, is already obtained in the fourth set corresponding to the fourth term in A153588. [Edited by Rainer Rosenthal, Oct 27 2020]
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MAPLE
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# SetA174283(n) is the set of resistances counted by A174283(n) (see Maple link).
AccumulatedSetsA174283 := proc(n) option remember;
if n=1 then {1} else `union`(AccumulatedSetsA174283(n-1), SetA174283(n)) fi end:
A174284 := n -> nops(AccumulatedSetsA174283(n)):
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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