A357115 T(n,m) is the numerator of the resistance between two nodes located at the end of a side of length n 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 square array read by descending antidiagonals.
3, 11, 4, 41, 5, 13, 153, 26, 267, 26, 571, 68, 181, 192, 149, 2131, 89, 10609, 1506, 1171, 138, 7953, 466, 25059, 251, 155927, 246, 375, 29681, 1220, 3869723, 13852, 759435, 77948, 75255, 668, 110771, 1597, 1334085, 781778, 109897, 1949020, 982871, 24995, 3523
Offset: 1
Examples
The array of resistances starts:
3/4, 11/15, 41/56, 153/209, ... A001835(n-1)/A001353(n-1)
4/3, 5/4, 26/21, 68/55, ...
13/7, 267/161, 181/112, 10609/6603, ...
26/11, 192/95, 1506/781, 251/132, ...
149/52, 1171/495, 155927/70616, 759435/352583, ...
138/41, 246/91, 77948/31529, 1949020/817991, ...
.
T(1,3)/A357116(1,3) = 41/56:
. _____ _____ _____
O--|__1__|--O--|__1__|--O--|__1__|--O-----O
| | | | |
| | | | | | | | |
|1| |1| |1| |1| 41/56 ohms
|_| |_| |_| |_| |
| _____ | _____ | _____ | |
O--|__1__|--O--|__1__|--O--|__1__|--O-----O
.
T(3,1)/A357116(3,1) = 13/7 T(2,2)/A357116(2,2) = 5/4
. _____ _____ _____
O--|__1__|--O-----O O--|__1__|--O--|__1__|--O-----O
| | | | | | |
| | | | | | | | | | | |
|1| |1| | |1| |1| |1| |
|_| |_| | |_| |_| |_| |
| _____ | | | _____ | _____ | |
O--|__1__|--O | O--|__1__|--O--|__1__|--O 5/4 ohms
| | | | | | |
| | | | 13/7 | | | | | | |
|1| |1| ohms |1| |1| |1| |
|_| |_| | |_| |_| |_| |
| _____ | | | _____ | _____ | |
O--|__1__|--O | O--|__1__|--O--|__1__|--O-----O
| | |
| | | | |
|1| |1| |
|_| |_| |
| _____ | |
O--|__1__|--O-----O
Formula
Limit_{n->oo} T(1,n)/A357116(1,n) = sqrt(3) - 1.