cp's OEIS Frontend

A153588 Number of resistance values that can be constructed using up to n equal resistances by arranging them in an arbitrary series-parallel arrangement.

%I A153588 #53 Dec 08 2024 17:13:51
%S A153588 1,3,7,15,35,77,179,429,1039,2525,6235,15463,38513,96231,241519,
%T A153588 607339,1529533,3857447,9743247,24634043,62335495,157885967,400211085,
%U A153588 1015080877,2576308943,6542380707,16622493939,42252603207,107447022475,273337662943
%N A153588 Number of resistance values that can be constructed using up to n equal resistances by arranging them in an arbitrary series-parallel arrangement.
%H A153588 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 A153588 Sameen Ahmed Khan, <a href="/A153588/a153588.nb">Mathematica notebook for A153588 and A058351</a>
%H A153588 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>, arXiv:1004.3346 [physics.gen-ph], 2010.
%H A153588 Sameen Ahmed Khan, <a href="https://www.ias.ac.in/article/fulltext/reso/017/05/0468-0475">How Many Equivalent Resistances?</a>, RESONANCE, May 2012.
%H A153588 Sameen Ahmed Khan, <a href="https://dx.doi.org/10.17485/ijst/2016/v9i44/88086">Beginning to count the number of equivalent resistances</a>, Indian Journal of Science and Technology, 2016, Vol 9(44).
%H A153588 M. Ortolano, M. Abrate, and 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 [physics.ins-det], 2013.
%H A153588 Project Euler, <a href="http://projecteuler.net/index.php?section=problems&amp;id=155">Problem 155: Counting Capacitor Circuits</a>.
%e A153588 For n=2 there are 3 solutions, 1 ohm, (1+1) ohms and 1/(1/1+1/1)=1/2 ohm. So a(2)=3.
%Y A153588 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 A153588 Cf. A048211, A153588, A174283, A174284, A174285 and A174286, A176497, A176498, A176499, A176500, A176501, A176502. [_Sameen Ahmed Khan_, Apr 27 2010]
%K A153588 hard,more,nonn
%O A153588 1,2
%A A153588 Altrego Janeway (altrego99(AT)gmail.com), Dec 29 2008
%E A153588 a(17)-a(25) from _Antoine Mathys_, Apr 02 2015
%E A153588 Definition clarified by _Antoine Mathys_, Apr 03 2015
%E A153588 a(26)-a(30) from _Antoine Mathys_, Dec 08 2024