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%I #7 Dec 10 2020 07:20:07
%S 15,172,1114,5378,22321,83995,293744,968965
%N a(n) is the number of resistance values R=x/y that can be obtained by a network of at most n one-ohm resistors such that a network of more than n one-ohm resistors is needed to obtain the resistance y/x.
%C a(n) = 0 for n < 10.
%D Technology Review's Puzzle Corner, How many different resistances can be obtained by combining 10 one ohm resistors? Oct 3, 2003.
%H Joel Karnofsky, <a href="http://cs.nyu.edu/~gottlieb/tr/overflow/2003-dec-2.pdf">Solution of problem from Technology Review's Puzzle Corner Oct 3, 2003</a>, Feb 23 2004.
%e a(10) = 15: this is the number of non-reciprocal resistance values provided in Karnofsky's solution of the 10-resistors puzzle. The list of 15 resistances is: 95/106, 101/109, 98/103, 97/98, 103/101, 97/86, 110/91, 103/83, 130/101, 103/80, 115/89, 106/77, 109/77, 98/67, 101/67.
%e a(11) = 172: the corresponding resistances are provided in A338581/A338591.
%e a(12) = 1114: the corresponding resistances are provided in A338582/A338592.
%Y Cf. A180414, A338573, A338601, A338602, A338581, A338591, A338582, A338592.
%K nonn,hard,more
%O 10,1
%A _Hugo Pfoertner_, Dec 10 2020