A339547 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.

15, 172, 1114, 5378, 22321, 83995, 293744, 968965

Offset: 10

Author

Hugo Pfoertner, Dec 10 2020

Keywords

• nonn
• hard
• more

Comments

a(n) = 0 for n < 10.

Examples

			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.
a(11) = 172: the corresponding resistances are provided in A338581/A338591.
a(12) = 1114: the corresponding resistances are provided in A338582/A338592.
		

References

• Technology Review's Puzzle Corner, How many different resistances can be obtained by combining 10 one ohm resistors? Oct 3, 2003.

Links

• Joel Karnofsky, Solution of problem from Technology Review's Puzzle Corner Oct 3, 2003, Feb 23 2004.

Crossrefs

Cf. A180414, A338573, A338601, A338602, A338581, A338591, A338582, A338592.