A357113 - OEIS

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.

%I #6 Sep 16 2022 13:22:57

%S 1,7,3,15,121,13,45,430,2089,47,43,1047,37873,2749,1171,239,7148,

%T 321249,10499426,2905619,6385,433,33647,59557,156300899,9176362943,

%U 766114047605,982871,1157,13971,15887065,1637345324,120912032349,25420198613182,771357156007,441083

%N 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.

%e The triangle of resistances begins:

%e 1;

%e 7/5, 3/2;

%e 15/8, 121/69, 13/7;

%e 45/19, 430/209, 2089/1023, 47/22;

%e 43/15, 1047/440, 37873/16744, 2749/1205, 1171/495

%e .

%e O- 1 ohm -O

%e | |

%e O-===-O |

%e # # |

%e O-===-O---'

%e .

%e O-- 7/5 ohms ---O O--- 3/2 ohms --O

%e | | | |

%e O-===-O-===-O | O-===-O-===-O |

%e # # # | # # # |

%e O-===-O-===-O---' O-===-O-===-O |

%e # # # |

%e O-===-O-===-O---'

%e .

%e O---- 15/8 ohms ------O O--- 121/69 ohms -----O O--- 13/7 ohms -------O

%e | | | | | |

%e O-===-O-===-O-===-O | O-===-O-===-O-===-O | O-===-O-===-O-===-O |

%e # # # # | # # # # | # # # # |

%e O-===-O-===-O-===-O---' O-===-O-===-O-===-O | O-===-O-===-O-===-O |

%e # # # # | # # # # |

%e O-===-O-===-O-===-O---' O-===-O-===-O-===-O |

%e # # # # |

%e O-===-O-===-O-===-O---'

%Y A357114 are the corresponding denominators.

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

%K nonn,frac,tabl

%O 1,2

%A _Hugo Pfoertner_, Sep 15 2022