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Search: id:A123750
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| A123750 |
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Number of distinct resistances possible with at most n arbitrary resistors connected in series or in parallel. |
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+0
1
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| 0, 1, 4, 17, 94, 667, 5752, 58053, 669970, 8698991, 125499820, 1991637529, 34479906886, 646671878595, 13061304372448, 282652185684845, 6524494505342842, 160018549741811479, 4155443426929596436
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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.
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LINKS
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I. N. Galidakis, Home Page (listed in lieu of email address)
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FORMULA
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a(n) = 2*A005840(n) + n - 2; generating function = exp(x)*(-2*exp(x) + exp(x)*x + 2)/(-2 + exp(x))
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EXAMPLE
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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, ...
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MAPLE
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series(exp(x)*(-2*exp(x) + exp(x)*x + 2)/(-2 + exp(x)), x, 8);
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CROSSREFS
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Cf. A005840. a(n) = 2*A005840(n) + n - 2, n > 1; A051045.
Adjacent sequences: A123747 A123748 A123749 this_sequence A123751 A123752 A123753
Sequence in context: A112354 A020011 A067084 this_sequence A024052 A128321 A091635
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KEYWORD
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nonn
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AUTHOR
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I. N. Galidakis (jgal(AT)ath.forthnet.gr), Nov 28 2006
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