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A117747
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Number of different configurations of cycles (loops) in graphs containing directed and undirected links.
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1
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7, 15, 30, 74, 171, 444, 1138, 3048, 8175, 22427, 61686, 171630, 479411
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| Examples of such graphs are cellular gene regulatory networks and signal transduction networks.
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REFERENCES
| 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
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LINKS
| Avi Ma'ayan, C program to produce sequence
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FORMULA
| 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.
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EXAMPLE
| a(3) = 1/6 *(3^3+3^1+3^1) + 3^(2/2) / 2 = 7
a(4) = 1/8 * (3^4+3^1+3^2+3^1) + 3^(4/2) / 3 = 15
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.
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CROSSREFS
| Cf. A000011.
Sequence in context: A006188 A198589 A139597 * A179882 A137196 A120094
Adjacent sequences: A117744 A117745 A117746 * A117748 A117749 A117750
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KEYWORD
| nonn
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AUTHOR
| 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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