A153588 Number of resistance values that can be constructed using up to n equal resistances by arranging them in an arbitrary series-parallel arrangement.

1, 3, 7, 15, 35, 77, 179, 429, 1039, 2525, 6235, 15463, 38513, 96231, 241519, 607339, 1529533, 3857447, 9743247, 24634043, 62335495, 157885967, 400211085, 1015080877, 2576308943

Offset

1,2

Links

Table of n, a(n) for n=1..25.

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, Mathematica notebook for A153588 and A058351

Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, arXiv:1004.3346 [physics.gen-ph], 2010.

Sameen Ahmed Khan, How Many Equivalent Resistances?, RESONANCE, May 2012.

Sameen Ahmed Khan, Beginning to count the number of equivalent resistances, Indian Journal of Science and Technology, 2016, Vol 9(44).

M. Ortolano, M. Abrate, and L. Callegaro, On the synthesis of Quantum Hall Array Resistance Standards, arXiv preprint arXiv:1311.0756 [physics.ins-det], 2013.

Project Euler, Problem 155: Counting Capacitor Circuits.

Example

Example: For n=2 there are 3 solutions, 1 ohm, (1+1) ohms and 1/(1/1+1/1)=1/2 ohm.

Crossrefs

Cf. A048211. This sequence is the total number of resistance values formed using up to n resistances, A048211 is the total number of resistance values formed using exactly n resistances.

Cf. A048211, A153588, A174283, A174284, A174285 and A174286, A176497, A176498, A176499, A176500, A176501, A176502. [Sameen Ahmed Khan, Apr 27 2010]

Sequence in context: A213722 A325924 A217092 * A221945 A077946 A077970

Adjacent sequences: A153585 A153586 A153587 * A153589 A153590 A153591

Keyword

hard,more,nonn

Author

Altrego Janeway (altrego99(AT)gmail.com), Dec 29 2008

Extensions

a(17)-a(25) from Antoine Mathys, Apr 02 2015

Definition clarified by Antoine Mathys, Apr 03 2015

Status

approved