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A176501 Farey(m; I) where m = Fibonacci (n + 1) and I = [1/n, 1]. 12
1, 2, 4, 9, 19, 50, 122, 317, 837, 2213, 5758, 15236, 40028, 105079, 276627, 727409, 1910685, 5020094 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence arises in the analytically obtained strict upper bound of the set of equivalent resistances formed by any conceivable network (series/parallel or bridge, or non-planar) of n equal resistors. Consequently it provides an strict upper bound of the sequences: A048211, A153588, A174283, A174284, A174285 and A174286. This strict upper bound provided by this difficult to compute (due to computer memory) sequence is better than the easier to compute Sequence A176499.

LINKS

Table of n, a(n) for n=1..18.

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), 175-179 (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.gen-ph], (20 April 2010).

Sameen Ahmed Khan, Mathematica notebook

EXAMPLE

n = 5, I = [1/5, 1], m = Fibonacci(5 + 1) = 8, Farey(8) = 23, Farey(8; I) = 19

CROSSREFS

Cf. A048211, A153588, A174283, A174284, A174285 and A174286, A176499, A176500, A176502.

Sequence in context: A000080 A153447 A076893 * A096354 A076838 A034749

Adjacent sequences:  A176498 A176499 A176500 * A176502 A176503 A176504

KEYWORD

more,nonn

AUTHOR

Sameen Ahmed Khan, Apr 21 2010

STATUS

approved

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Last modified May 6 13:01 EDT 2016. Contains 272502 sequences.