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A176502 2*Farey(m; I) - 1 where m = Fibonacci (n + 1) and I = [1/n, 1]. 14
1, 3, 7, 17, 37, 99, 243, 633, 1673, 4425, 11515, 30471, 80055, 210157, 553253, 1454817, 3821369, 10040187 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence provides a 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 A176500.

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, Integer Sequences Authored by Dr. Sameen Ahmed Khan

Sameen Ahmed Khan, Mathematica notebook

S. A. Khan, How Many Equivalent Resistances?, RESONANCE, May 2012. - From N. J. A. Sloane, Oct 15 2012

S. A. Khan, Farey sequences and resistor networks, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 153-162. - From N. J. A. Sloane, Oct 23 2012

EXAMPLE

n = 5, , I = [1/5, 1], m = Fibonacci(6) = 8, Farey(8) = 23, Farey(8; I) = 19, Grand Set(5) = 37.

CROSSREFS

Cf. A048211, A153588, A174283, A174284, A174285 and A174286, A176499, A176500, A176501.

Sequence in context: A178941 A178155 A026396 * A141199 A003478 A119587

Adjacent sequences:  A176499 A176500 A176501 * A176503 A176504 A176505

KEYWORD

more,nonn

AUTHOR

Sameen Ahmed Khan, Apr 21 2010

STATUS

approved

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Last modified June 26 14:42 EDT 2017. Contains 288766 sequences.