%I #6 Nov 19 2013 12:37:09
%S 1,2,8,48,386,3781,49475,762869,13554897,266817541
%N Number of distinct resistances that can be produced from a circuit of resistors with resistances 1, 2, ..., n using only series and parallel combinations.
%C Found by exhaustive search: all configurations of resistors were enumerated, resistances calculated, sorted, and distinct values counted.
%C 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.
%C 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.
%C This sequence considers resistors with contiguous resistances 1, 2, ..., n; A005840 considers arbitrarily different resistors, while A048211 considers n equal resistances.
%e 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.
%Y Cf. A005840, A006352, A048211, A051045.
%K nonn,more
%O 1,2
%A _Dave R.M. Langers_, Nov 16 2013