Search: id:A117747
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%I A117747
%S A117747 7,15,30,74,171,444,1138,3048,8175,22427,61686,171630,479411
%N A117747 Number of different configurations of cycles (loops) in graphs containing 
               directed and undirected links.
%C A117747 Examples of such graphs are cellular gene regulatory networks and signal 
               transduction networks.
%D A117747 Ma'ayan, A., Jenkins, S. L., Neves, S., Hasseldine, A., Grace, E., Dubin-Thaler, 
               B., Eungdamrong, N. J., Weng, G., Ram, P. T., Rice, J. J., Kershenbaum, 
               A., Stolovitzky, G. A., Blitzer, R. D. and Iyengar, R., Formation 
               of regulatory patterns during signal propagation in a Mammalian cellular 
               network. Science. 2005 Aug 12;309
%H A117747 Avi Ma'ayan, <a href="a117747.txt">C program to produce sequence</a>
%F A117747 a(n) = 1/(2*n) (sum from k=0 to k=n-1 of (3^gcd(n,k)) + (3^(n/2))/ 3 
               if n is even, a(n) = 1/(2*n) (sum from k=0 to k=n-1 of (3^gcd(n,k)) 
               + (3^((n-1)/2))/ 2 if n is odd, where gcd is the greatest common 
               divisor and gcd(n, 0) equals n. See code below. Also a(n) = 3^n / 
               (2*n) gives a good approximation for large n.
%e A117747 a(3) = 1/6 *(3^3+3^1+3^1) + 3^(2/2) / 2 = 7
%e A117747 a(4) = 1/8 * (3^4+3^1+3^2+3^1) + 3^(4/2) / 3 = 15
%e A117747 The 7 cycles of length 3 are: --> 0 --> 0 --> 0, --> 0 <-- 0 --> 0, -0 
               --> 0 --> 0, -0 --> 0 <-- 0, -0 <-- 0 --> 0, -0-0 --> 0, -0-0-0.
%Y A117747 Cf. A000011.
%Y A117747 Sequence in context: A146624 A006188 A139597 this_sequence A137196 A120094 
               A078485
%Y A117747 Adjacent sequences: A117744 A117745 A117746 this_sequence A117748 A117749 
               A117750
%K A117747 nonn
%O A117747 3,1
%A A117747 Avi Ma'ayan (avi.maayan(AT)mssm.edu), Guillermo Cecchi, John Wagner, 
               Ravi Rao, Azi Lipshtat, Ravi Iyengar and Gustavo Stolovitzky, Apr 
               28 2006

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