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.

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.

Links

Table of n, a(n) for n=2..20.

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

Cf. A010357, A337517.

Sequence in context: A292211 A293348 A188287 * A148281 A148282 A148283

Adjacent sequences: A363237 A363238 A363239 * A363241 A363242 A363243

Keyword

nonn,more

Author

Zhao Hui Du, May 23 2023

Status

approved