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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. 14
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)



Table of n, a(n) for n=1..25.

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, Mathematica notebook for A153588 and A058351

Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, E-Print arXiv:1004.3346 (21 April 2010).

S. A. Khan, How Many Equivalent Resistances?, RESONANCE, May 2012. - From N. J. A. Sloane, Oct 15 2012

M. Ortolano, M. Abrate, L. Callegaro, On the synthesis of Quantum Hall Array Resistance Standards, arXiv preprint arXiv:1311.0756, 2013

Project Euler, Problem 155


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.

A048211, A153588, A174283, A174284, A174285 and A174286, A176497, A176498, A176499, A176500, A176501, A176502 [From Sameen Ahmed Khan, Apr 27 2010]

Sequence in context: A147379 A213722 A217092 * A221945 A077946 A077970

Adjacent sequences:  A153585 A153586 A153587 * A153589 A153590 A153591




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 May 26 08:55 EDT 2017. Contains 287093 sequences.