A357113 T(n,m) is the numerator 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, 7, 3, 15, 121, 13, 45, 430, 2089, 47, 43, 1047, 37873, 2749, 1171, 239, 7148, 321249, 10499426, 2905619, 6385, 433, 33647, 59557, 156300899, 9176362943, 766114047605, 982871, 1157, 13971, 15887065, 1637345324, 120912032349, 25420198613182, 771357156007, 441083

Offset

1,2

Links

Table of n, a(n) for n=1..36.

Example

The triangle of resistances 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
.
  O- 1 ohm -O
  |         |
  O-===-O   |
  #     #   |
  #     #   |
  O-===-O---'
.
  O-- 7/5 ohms ---O        O--- 3/2 ohms --O
  |               |        |               |
  O-===-O-===-O   |        O-===-O-===-O   |
  #     #     #   |        #     #     #   |
  #     #     #   |        #     #     #   |
  O-===-O-===-O---'        O-===-O-===-O   |
                           #     #     #   |
                           #     #     #   |
                           O-===-O-===-O---'
.
  O---- 15/8 ohms ------O  O--- 121/69 ohms -----O  O--- 13/7 ohms -------O
  |                     |  |                     |  |                     |
  O-===-O-===-O-===-O   |  O-===-O-===-O-===-O   |  O-===-O-===-O-===-O   |
  #     #     #     #   |  #     #     #     #   |  #     #     #     #   |
  #     #     #     #   |  #     #     #     #   |  #     #     #     #   |
  O-===-O-===-O-===-O---'  O-===-O-===-O-===-O   |  O-===-O-===-O-===-O   |
                           #     #     #     #   |  #     #     #     #   |
                           #     #     #     #   |  #     #     #     #   |
                           O-===-O-===-O-===-O---'  O-===-O-===-O-===-O   |
                                                    #     #     #     #   |
                                                    #     #     #     #   |
                                                    O-===-O-===-O-===-O---'

Crossrefs

A357114 are the corresponding denominators.

Cf. A093652, A212045, A212046, A357115, A357116.

Sequence in context: A195159 A279353 A200943 * A283289 A357200 A284477

Adjacent sequences: A357110 A357111 A357112 * A357114 A357115 A357116

Keyword

nonn,frac,tabl

Author

Hugo Pfoertner, Sep 15 2022

Status

approved