Search: id:A123750
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%I A123750
%S A123750 0,1,4,17,94,667,5752,58053,669970,8698991,125499820,1991637529,
%T A123750 34479906886,646671878595,13061304372448,282652185684845,
%U A123750 6524494505342842,160018549741811479,4155443426929596436
%N A123750 Number of distinct resistances possible with at most n arbitrary resistors 
               connected in series or in parallel.
%C A123750 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.
%H A123750 I. N. Galidakis, <a href="http://ioannis.virtualcomposer2000.com/">Home 
               Page (listed in lieu of email address)</a>
%F A123750 a(n) = 2*A005840(n) + n - 2; generating function = exp(x)*(-2*exp(x) 
               + exp(x)*x + 2)/(-2 + exp(x))
%e A123750 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, ...
%p A123750 series(exp(x)*(-2*exp(x) + exp(x)*x + 2)/(-2 + exp(x)),x,8);
%Y A123750 Cf. A005840. a(n) = 2*A005840(n) + n - 2, n > 1; A051045.
%Y A123750 Sequence in context: A112354 A020011 A067084 this_sequence A024052 A128321 
               A091635
%Y A123750 Adjacent sequences: A123747 A123748 A123749 this_sequence A123751 A123752 
               A123753
%K A123750 nonn
%O A123750 1,3
%A A123750 I. N. Galidakis (jgal(AT)ath.forthnet.gr), Nov 28 2006

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