A357114 T(n,m) is the denominator of the resistance between two diametrically opposite nodes of a rectangular electric network of n*m quadratic meshes in which all edges are replaced by one-ohm resistors, where T(n,m) is a triangle read by rows.

1, 5, 2, 8, 69, 7, 19, 209, 1023, 22, 15, 440, 16744, 1205, 495, 71, 2639, 128617, 4282081, 1169441, 2494, 112, 11067, 21728, 59292739, 3498175408, 287916805961, 360161, 265, 4142, 5317209, 579080689, 43600867640, 9153575734849, 273893674761, 153254

Offset: 1

Author

Hugo Pfoertner, Sep 15 2022

Keywords

• nonn
• frac
• tabl

Examples

			The triangle begins:
   1;
   7/5,       3/2;
  15/8,     121/69,      13/7;
  45/19,   430/209,   2089/1023,     47/22;
  43/15,  1047/440,  37873/16744,  2749/1205,  1171/495
		

Links

• MingKun Yue, Rows n=1..24 of triangle, flattened

Crossrefs

A357113 are the corresponding numerators.

Programs

Mathematica

ResistanceDistance[g_Graph,i_Integer,j_Integer]:=Module[{n=VertexCount[g]},ResistanceDistanceMatrix=PseudoInverse[KirchhoffMatrix[g]+ConstantArray[1/n,{n,n}]];ResistanceDistanceMatrix[[i,i]]+ResistanceDistanceMatrix[[j,j]]-ResistanceDistanceMatrix[[i,j]]-ResistanceDistanceMatrix[[j,i]]]; a[n_Integer,m_Integer]:=ResistanceDistance[GridGraph[{n,m}],1,n*m]; Denominator[Flatten[Table[a[n,m],{n,2,10},{m,2,n}]]] (* MingKun Yue, Jan 25 2025 *)