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

Author

Zhao Hui Du, May 23 2023

Keywords

• nonn
• more

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.

Examples

			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.