A232005 Number of distinct resistances that can be produced from a circuit of resistors with resistances 1, 2, ..., n using only series and parallel combinations.

1, 2, 8, 48, 386, 3781, 49475, 762869, 13554897, 266817541

Offset: 1

Author

Dave R.M. Langers, Nov 16 2013

Keywords

• nonn
• more

Comments

Found by exhaustive search: all configurations of resistors were enumerated, resistances calculated, sorted, and distinct values counted.

This sequence allows any circuits to be combined in series or in parallel (akin A000084); A051045 requires circuits to be combined with a single resistor at a time.

This sequence regards circuits as distinct only if their resistance is different; A006351 regards circuits distinct if their configuration is different, although some may have the same resistance.

This sequence considers resistors with contiguous resistances 1, 2, ..., n; A005840 considers arbitrarily different resistors, while A048211 considers n equal resistances.

Examples

			a(2) = 2 since given a 1-ohm and a 2-ohm resistor, a series circuit yields 3 ohms, while a parallel circuit yields 2/3 ohms, which thus yields two distinct resistances.
		

Crossrefs

Cf. A005840, A006352, A048211, A051045.