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, 6542380707, 16622493939, 42252603207, 107447022475, 273337662943

Offset: 1

Author

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

Keywords

• hard
• more
• nonn

Examples

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

Links

• 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.

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]

Extensions

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

Definition clarified by Antoine Mathys, Apr 03 2015

a(26)-a(30) from Antoine Mathys, Dec 08 2024