A338197 a(n) is the number of distinct resistances that can be obtained by a network of exactly n equal resistors, but not by any network with fewer than n equal resistors.

1, 2, 4, 8, 20, 44, 114, 312, 894, 2639, 8005, 24362, 74918, 231123, 722388, 2276599, 7242497, 23144119, 74203799, 238684352

Offset: 1

Author

Hugo Pfoertner, Nov 03 2020

Keywords

• nonn
• hard
• more

Comments

See A180414 and A337517 for more information and references.

Examples

			a(6) = 44 because the resistances 11/13 and 13/11 (in units of resistor value) are representable in addition to the A051389(6)=42 resistances that can be achieved by only serial and parallel configurations with exactly 6 resistors and not by a network with fewer than 6 resistors.
		

Links

• Allan Gottlieb, Oct 3, 2003 addendum (Karnofsky).
• Index to sequences related to resistances.

Crossrefs

Cf. A051389, A180414, A337517, A338487.

Formula

a(n) = A180414(n) - A180414(n-1).

a(n) = A051389(n) for n <= 5, a(n) > A051389(n) otherwise.

Extensions

a(15) corrected and a(16) added by Hugo Pfoertner, Dec 06 2020

a(17) from Hugo Pfoertner, Dec 09 2020

a(18) from Hugo Pfoertner, Apr 09 2021

a(19) from Zhao Hui Du, May 15 2023

a(20) from Zhao Hui Du, May 23 2023