

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, 420862602279, 1101832758583
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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 nonplanar) 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. AdamsWatters, 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), 175179 (February 2000). Digital Object Identifier (DOI): http://dx.doi.org/10.1119/1.19396


LINKS

Antoine Mathys, Table of n, a(n) for n = 1..49
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], (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.


MATHEMATICA

a[n_] := 2 Sum[EulerPhi[k], {k, 1, Fibonacci[n+1]}]  1;
Table[an = a[n]; Print[an]; an, {n, 1, 30}] (* JeanFrançois Alcover, Nov 03 2018, from PARI *)


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

a(26)a(28) from Sameen Ahmed Khan, May 02 2010
a(29)a(30) from Antoine Mathys, Aug 06 2018


STATUS

approved



