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n = 3:
Networks with 3 unit resistors have A337517(3) = 4 resistance values: {1/3, 3, 3/2, 2/3}. The maximum product numerator x denominator is 6.
n = 6:
Networks with 6 unit resistors have A337517(6) = 57 resistance values, where 11/13 and 13/11 are the resistances with maximum product numerator x denominator.
+-----------+-------------+
A | | |
/ \ | | |
(1) / \ (2) | 6 X 6 | 7 X 7 |
/ \ | | |
/ (3) \ | | |
o---------o +---------+-+ |
\ // | +-+-----+-------+
\ (5)// | 5 X 5 | | |
(4) \ //(6) | | 4 X 4 | 4 X 4 |
\ // | | | |
Z +---------+-------+-------+
___________________________________________________________________
Network with 6 unit resistors Corresponding rectangle tiling
total resistance 11/13 giving with 6 squares giving
a(6) = 11 x 13 = 143 A338861(6) = 143
n = 10:
With n = 10, non-planarity comes in, yielding a(10) > A338861(10).
The "culprit" here is the network with resistance A338601(9)/A338602(9) = 130/101, giving a(10) = 13130 > A338861(10) = 10920.
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