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

1,2

Links

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

Example

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

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 *)

Crossrefs

A357113 are the corresponding numerators.

Sequence in context: A198192 A046878 A375600 * A078335 A021658 A270859

Adjacent sequences: A357111 A357112 A357113 * A357115 A357116 A357117

Keyword

nonn,frac,tabl

Author

Hugo Pfoertner, Sep 15 2022

Status

approved