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A153588 Number of resistance values that can be constructed using up to n equal resistances by arranging them in an arbitrary series-parallel arrangement. 17
1, 3, 7, 15, 35, 77, 179, 429, 1039, 2525, 6235, 15463, 38513, 96231, 241519, 607339, 1529533, 3857447, 9743247, 24634043, 62335495, 157885967, 400211085, 1015080877, 2576308943 (list; graph; refs; listen; history; text; internal format)
Antoni Amengual, The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel, American Journal of Physics, 68(2), 175-179 (February 2000).
Sameen Ahmed Khan, How Many Equivalent Resistances?, RESONANCE, May 2012.
Sameen Ahmed Khan, Beginning to count the number of equivalent resistances, Indian Journal of Science and Technology, 2016, Vol 9(44).
M. Ortolano, M. Abrate, and L. Callegaro, On the synthesis of Quantum Hall Array Resistance Standards, arXiv preprint arXiv:1311.0756 [physics.ins-det], 2013.
Example: For n=2 there are 3 solutions, 1 ohm, (1+1) ohms and 1/(1/1+1/1)=1/2 ohm.
Cf. A048211. This sequence is the total number of resistance values formed using up to n resistances, A048211 is the total number of resistance values formed using exactly n resistances.
Sequence in context: A213722 A325924 A217092 * A221945 A077946 A077970
Altrego Janeway (altrego99(AT)gmail.com), Dec 29 2008
a(17)-a(25) from Antoine Mathys, Apr 02 2015
Definition clarified by Antoine Mathys, Apr 03 2015

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Last modified December 5 10:56 EST 2023. Contains 367589 sequences. (Running on oeis4.)