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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, 420862602279, 1101832758583 (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. A176502 provides a better strict upper bound but is harder to compute. [Corrected by Antoine Mathys, Jul 12 2019] Farey(n) = A005728(n). - Franklin T. Adams-Watters, May 12 2010 LINKS Antoine Mathys, Table of n, a(n) for n = 1..50 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], (Apr 20 2010). Sameen Ahmed KHAN, Mathematica notebook 1 Sameen Ahmed KHAN, Mathematica notebook 2 FORMULA a(n) = 2 * A176499(n) - 3. 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}] (* Jean-François Alcover, Nov 03 2018, from PARI *) PROG (PARI) a(n) = 2*sum(k=1, fibonacci(n+1), eulerphi(k))-1 \\ Charles R Greathouse IV, Oct 07 2016 (MAGMA) [2*(&+[EulerPhi(k):k in [1..Fibonacci(n+1)]])-1:n in [1..30]]; // Marius A. Burtea, Jul 26 2019 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

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Last modified October 23 12:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)