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A363240
Number of distinct resistances that can be produced from a circuit that is a 2-connected loopless multigraph with n edges and each edge having a unit resistor.
0
1, 2, 5, 12, 32, 88, 260, 819, 2680, 8642, 27976, 88946, 281541, 893028, 2841344, 9092174, 29176634, 93854841, 302611365
OFFSET
2,2
COMMENTS
The resistances between any two nodes of the graph are counted.
All resistances in A337517 can be obtained by serial combinations of resistances of one or more 2-connected loopless multigraphs.
EXAMPLE
a(2)=1 since the only multigraph with 2 edges is a double edge graph which forms resistance 1/2.
For n=4, there are a quadruple edge graph (resistance 1/4), a triangle graph with one double edge (2/5 between double edge and 3/5 between single edge) and square graph (3/4 between neighbor nodes and 1 between opposite nodes) so a(4)=5.
CROSSREFS
Sequence in context: A292211 A293348 A188287 * A148281 A148282 A148283
KEYWORD
nonn,more
AUTHOR
Zhao Hui Du, May 23 2023
STATUS
approved