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A176500 a(n) = 2*Farey(Fibonacci(n + 1)) - 3. 13
1, 3, 7, 19, 43, 115, 279, 719, 1879, 4911, 12659, 33235, 86715, 226315, 592767, 1551791, 4060203, 10630767, 27825227, 72843667, 190710291, 499271047, 1307051711, 3421933647, 8958716547, 23453948495, 61403187051, 160755514791 (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. A better strict bound is obtained by the Sequence A176502, but it is difficult to compute due to memory limitations.

Farey(n) = A005728(n). - Franklin T. Adams-Watters, May 12 2010

REFERENCES

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). Digital Object Identifier (DOI): http://dx.doi.org/10.1119/1.19396

LINKS

Table of n, a(n) for n=1..28.

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], (Apr 20 2010).

Sameen Ahmed KHAN, Mathematica notebook 1

Sameen Ahmed KHAN, Mathematica notebook 2

EXAMPLE

n = 5, m = Fibonacci(5 + 1) = 8, Farey(8) = 23, 2Farey(m) - 3 = 43.

PROG

((PARI) 2*sum(k=1, fibonacci(n+1), eulerphi(k))-1 \\ Charles R Greathouse IV, Oct 07 2016

CROSSREFS

Cf. A048211, A153588, A174283, A174284, A174285, A174286, A176499, A176501, A176502.

Sequence in context: A192301 A055622 A075900 * A136041 A146685 A146653

Adjacent sequences:  A176497 A176498 A176499 * A176501 A176502 A176503

KEYWORD

nonn

AUTHOR

Sameen Ahmed Khan, Apr 21 2010

EXTENSIONS

Added four terms: 26 to 29. Sameen Ahmed Khan, May 02 2010

STATUS

approved

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Last modified June 28 15:21 EDT 2017. Contains 288839 sequences.