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

1,2

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.

Links

Table of n, a(n) for n=1..20.

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)).

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);

Crossrefs

Cf. A005840, A051045.

Sequence in context: A239914 A323664 A067084 * A278644 A249078 A353546

Adjacent sequences: A123747 A123748 A123749 * A123751 A123752 A123753

Keyword

nonn,uned

Author

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

Status

approved