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

1, 4, 17, 94, 667, 5752, 58053, 669970, 8698991, 125499820, 1991637529, 34479906886, 646671878595, 13061304372448, 282652185684845, 6524494505342842, 160018549741811479, 4155443426929596436, 113905714869793400001, 3286624199431263921838

Offset: 1

Author

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

Keywords

• nonn
• uned

Comments

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.

Crossrefs

Cf. A005840, A051045.

Programs

Maple

a:= n-> n!* coeff(series(exp(x)*(-2*exp(x) +
            exp(x)*x + 2)/(-2 + exp(x)), x, n+1),x,n):
seq(a(n), n=1..25);

Formula

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

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