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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

%I

%S 1,3,7,15,35,77,179,429,1039,2525,6235,15463,38513,96231,241519,

%T 607339,1529533,3857447,9743247,24634043,62335495,157885967,400211085,

%U 1015080877,2576308943

%N Number of resistance values that can be constructed using up to n equal resistances by arranging them in an arbitrary series-parallel arrangement.

%D Sameen Ahmed Khan, Beginning to count the number of equivalent resistances, Indian Journal of Science and Technology, 2016, Vol 9(44), DOI: 10.17485/ijst/2016/v9i44/88086, http://www.indjst.org/index.php/indjst/article/viewFile/88086/75398

%H Antoni Amengual, <a href="http://dx.doi.org/10.1119/1.19396">The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel</a>, American Journal of Physics, 68(2), 175-179 (February 2000).

%H Sameen Ahmed Khan, <a href="/A153588/a153588.nb">Mathematica notebook for A153588 and A058351</a>

%H Sameen Ahmed Khan, <a href="http://arxiv.org/abs/1004.3346">The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel</a>, E-Print arXiv:1004.3346 (21 April 2010).

%H S. A. Khan, <a href="http://www.ias.ac.in/resonance/May2012/p468-475.pdf">How Many Equivalent Resistances?</a>, RESONANCE, May 2012.

%H M. Ortolano, M. Abrate, L. Callegaro, <a href="http://arxiv.org/abs/1311.0756">On the synthesis of Quantum Hall Array Resistance Standards</a>, arXiv preprint arXiv:1311.0756, 2013

%H Project Euler, <a href="http://projecteuler.net/index.php?section=problems&amp;id=155">Problem 155</a>

%e Example: For n=2 there are 3 solutions, 1 ohm, (1+1) ohms and 1/(1/1+1/1)=1/2 ohm.

%Y 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.

%Y A048211, A153588, A174283, A174284, A174285 and A174286, A176497, A176498, A176499, A176500, A176501, A176502 [From _Sameen Ahmed Khan_, Apr 27 2010]

%K hard,more,nonn

%O 1,2

%A Altrego Janeway (altrego99(AT)gmail.com), Dec 29 2008

%E a(17)-a(25) from _Antoine Mathys_, Apr 02 2015

%E Definition clarified by _Antoine Mathys_, Apr 03 2015

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)