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A123750 Number of distinct resistances possible with at most n arbitrary resistors connected in series or in parallel. 0

%I

%S 1,4,17,94,667,5752,58053,669970,8698991,125499820,1991637529,

%T 34479906886,646671878595,13061304372448,282652185684845,

%U 6524494505342842,160018549741811479,4155443426929596436,113905714869793400001,3286624199431263921838

%N Number of distinct resistances possible with at most n arbitrary resistors connected in series or in parallel.

%C The difference between this problem and A005840 and A051045 is the word "at most". In this problem, at most n different resistors are used to generate all possible resistances using in series and in parallel wirings, also including resistances where some of the resistors from the collection 1,2,...,n, are not used.

%F a(n) = 2 * A005840(n) + n - 2, n > 1.

%F E.g.f.: exp(x)*(-2*exp(x) + exp(x)*x + 2)/(-2 + exp(x)).

%p a:= n-> n!* coeff(series(exp(x)*(-2*exp(x) +

%p exp(x)*x + 2)/(-2 + exp(x)), x, n+1),x,n):

%p seq(a(n), n=1..25);

%Y Cf. A005840, A051045.

%K nonn,uned

%O 1,2

%A I. N. Galidakis (jgal(AT)ath.forthnet.gr), Nov 28 2006

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Last modified August 14 13:43 EDT 2022. Contains 356117 sequences. (Running on oeis4.)