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A176498
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Number of elements less than 1/2 in the Cross Set which is the subset of the set of distinct resistances that can be produced using n equal resistors in series and/or parallel.
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3
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0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 9, 24, 58, 124, 312, 759, 1768, 4421, 10811, 27191, 68591, 174627, 441633, 1124795, 2866004
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OFFSET
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1,10
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COMMENTS
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This sequence arises in the decomposition of the sets A(n + 1) of equivalent resistances, when n equal resistors are combined in series/parallel, into series parallel and cross sets respectively. All the elements of the parallel set are strictly less than 1 and all those of the series set are strictly greater than 1. The cross set is expected to be dense around 1 with very few elements below 1/2. Hence it is relevant to count the elements below 1/2.
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LINKS
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EXAMPLE
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The order of the cross set is given by A176497: 0, 0, 0, 1, 4, 9, 25, 75, 195, 475, 1265, 3135, ... The sets corresponding n = 4 to n = 8 do not have a single element below 1/2. For n = 9 onwards we have a few elements which are less than 1/2; they are 1, 6, 9, 24, ....
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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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