cp's OEIS Frontend

A176498 Number of elements less than 1/2 in the Cross Set which is the subset of the set of distinct resistances that can be produced using n unit resistors in series and/or parallel.

%I A176498 #33 Dec 21 2024 00:46:04
%S A176498 0,0,0,0,0,0,0,0,1,6,9,24,58,124,312,759,1768,4421,10811,27191,68591,
%T A176498 174627,441633,1124795,2866004,7297500,18585359,47337643,120562041,
%U A176498 307063757
%N A176498 Number of elements less than 1/2 in the Cross Set which is the subset of the set of distinct resistances that can be produced using n unit resistors in series and/or parallel.
%C A176498 This sequence arises in the decomposition of the sets A(n + 1) of equivalent resistances, when n equal resistors are combined in series/parallel, into series parallel and cross sets respectively. All the elements of the parallel set are strictly less than 1 and all those of the series set are strictly greater than 1. The cross set is expected to be dense around 1 with very few elements below 1/2. Hence it is relevant to count the elements below 1/2.
%H A176498 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 A176498 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:1004.3346v1 [physics.gen-ph], (20 April 2010).
%H A176498 S. A. Khan, <a href="http://www.ias.ac.in/article/fulltext/pmsc/122/02/0153-0162">Farey sequences and resistor networks</a>, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 153-162. - _N. J. A. Sloane_, Oct 23 2012
%e A176498 The order of the cross set is given by A176497: 0, 0, 0, 1, 4, 9, 25, 75, 195, 475, 1265, 3135, ... The sets corresponding n = 4 to n = 8 do not have a single element below 1/2. For n = 9 onwards we have a few elements which are less than 1/2; they are 1, 6, 9, 24, ....
%Y A176498 Cf. A048211, A176497.
%K A176498 more,nonn
%O A176498 1,10
%A A176498 _Sameen Ahmed Khan_, Apr 21 2010
%E A176498 a(16)-a(25) from _Antoine Mathys_, Mar 20 2017
%E A176498 a(26)-a(30) from _Antoine Mathys_, Dec 08 2024