

A123750


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


0



0, 1, 4, 17, 94, 667, 5752, 58053, 669970, 8698991, 125499820, 1991637529, 34479906886, 646671878595, 13061304372448, 282652185684845, 6524494505342842, 160018549741811479, 4155443426929596436
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OFFSET

1,3


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..19.
I. N. Galidakis, Home Page (listed in lieu of email address)


FORMULA

a(n) = 2*A005840(n) + n  2; generating function = exp(x)*(2*exp(x) + exp(x)*x + 2)/(2 + exp(x))


EXAMPLE

exp(x)*(2*exp(x) + exp(x)*x + 2)/(2 + exp(x)) = 1*x + 2*x^2 + 17/6*x^3 + 47/12*x^4 + 667/120*x^5 + 719/90*x^6 + 19351/1680*x^7 + O(x^8); then the coefficients are multiplied by n! to get 1, 4, 17, 94, 667, 5752, 58053, 669970, 8698991, ...


MAPLE

series(exp(x)*(2*exp(x) + exp(x)*x + 2)/(2 + exp(x)), x, 8);


CROSSREFS

Cf. A005840. a(n) = 2*A005840(n) + n  2, n > 1; A051045.
Sequence in context: A020011 A239914 A067084 * A278644 A249078 A024052
Adjacent sequences: A123747 A123748 A123749 * A123751 A123752 A123753


KEYWORD

nonn


AUTHOR

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


STATUS

approved



