

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 equal resistors in series and/or parallel.


3



0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 9, 24, 58, 124, 312, 759, 1768, 4421, 10811, 27191, 68591, 174627, 441633, 1124795, 2866004
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OFFSET

1,10


COMMENTS

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.


LINKS

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), 175179 (February 2000).
Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, arXiv:1004.3346v1 [physics.genph], (20 April 2010).
S. A. Khan, Farey sequences and resistor networks, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 153162.  N. J. A. Sloane, Oct 23 2012


EXAMPLE

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, ....


CROSSREFS

Cf. A048211, A176497.
Sequence in context: A215528 A155577 A084431 * A142877 A260168 A093153
Adjacent sequences: A176495 A176496 A176497 * A176499 A176500 A176501


KEYWORD

more,nonn


AUTHOR

Sameen Ahmed Khan, Apr 21 2010


EXTENSIONS

a(16)a(25) from Antoine Mathys, Mar 20 2017


STATUS

approved



