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%I #61 May 23 2023 04:15:14
%S 1,2,4,8,16,36,80,194,506,1400,4039,12044,36406,111324,342447,1064835,
%T 3341434,10583931,33728050,107931849,346616201
%N Number of different resistances that can be obtained by combining n one-ohm resistors.
%C In "addendum" J. Karnofsky stated the value a(15) = 1064833. In contrast to the terms up to and including a(14), which could all be confirmed, an independent calculation based on a list of 3-connected simple graphs resulted in the corrected value a(15) = 1064835. - _Hugo Pfoertner_, Dec 06 2020
%C See A337517 for the number of different resistances that can be obtained by combining /exactly/ n one-ohm resistors. The method used by Andrew Howroyd (see his program in the link section) uses 3-connected graphs with one edge (the 'battery edge') removed. - _Rainer Rosenthal_, Feb 07 2021
%D Technology Review's Puzzle Corner, How many different resistances can be obtained by combining 10 one ohm resistors? Oct 3, 2003.
%H Allan Gottlieb, <a href="https://cs.nyu.edu/~gottlieb/tr/overflow/2003-oct-3-more.html">Oct 3, 2003 addendum (Karnofsky)</a>.
%H Andrew Howroyd, <a href="/A180414/a180414_2.txt">PARI program</a> (includes scripts for other related sequences)
%H Joel Karnofsky, <a href="http://cs.nyu.edu/~gottlieb/tr/overflow/2003-dec-2.pdf">Solution of problem from Technology Review's Puzzle Corner Oct 3, 2003</a>, Feb 23 2004.
%H Joel Karnofsky, <a href="/A180414/a180414_1.txt">Mathematica program for resistances</a>, copied from article.
%H <a href="/index/Res#resistances">Index to sequences related to resistances</a>.
%F a(n) = A174284(n) + 1 for n <= 7, a(n) > A174284(n) + 1 otherwise. - _Hugo Pfoertner_, Nov 01 2020
%F a(n) is the number of elements in the union of the sets SetA337517(k), k <= n, counted by A337517. - _Rainer Rosenthal_, Feb 07 2021
%e a(n) counts all resistances that can be obtained with fewer than n resistors as well as with exactly n resistors. Without a resistor the resistance is infinite, i.e., a(0) = 1. One 1-ohm resistor adds resistance 1, so a(1) = 2. Two resistors in parallel give 1/2 ohm, while in series they give 2 ohms. So a(2) is the number of elements in the set {infinity, 1, 1/2, 2}, i.e., a(2) = 4. - _Rainer Rosenthal_, Feb 07 2021
%t See link.
%Y Cf. A048211, A051389, A174284, A337517, A338197, A338487, A338573, A338580, A338590, A338600.
%Y Cf. A123545, A338511, A338999, A339072.
%K nonn,nice,hard,more
%O 0,2
%A _Vaclav Kotesovec_, Sep 02 2010
%E a(15) corrected and a(16) added by _Hugo Pfoertner_, Dec 06 2020
%E a(17) from _Hugo Pfoertner_, Dec 09 2020
%E a(0) from _Rainer Rosenthal_, Feb 07 2021
%E a(18) from _Hugo Pfoertner_, Apr 09 2021
%E a(19) from _Zhao Hui Du_, May 15 2023
%E a(20) from _Zhao Hui Du_, May 23 2023
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