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A119913
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Number of different simple cycles in the complete graph K_n; that is, the number of subsets of at least 3 elements out of n, ordered up to cyclic permutations.
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0
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0, 0, 2, 14, 74, 394, 2344, 16036, 125628, 1112028, 10976118, 119481218, 1421542550, 18348340022, 255323504812, 3809950976872, 60683990530072, 1027542662934744, 18430998766219146, 349096664728623126, 6962409983976703106, 145841989688186383106
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| a(n) = Sum_{k=3..n} (n choose k) * (k-1)!
a(n) = Sum_{i=2..n-1}(Floor(e*i!)) - (n+3)(n-2)/2
a(n) = Sum_{k=1..n-1} A038154(k)
a(n) = 2*A002807(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 04 2006
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EXAMPLE
| a(4)=14 because there are 6 4-cycles and 8 3-cycles.
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PROG
| Matlab: function a = an(n) s = 0; for i = 2:n-1 s = s+fix(exp(1)*factorial(i)); end a = s - (n+3)*(n-2)/2;
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CROSSREFS
| Cf. A038154.
Sequence in context: A138156 A192809 A198762 * A197874 A104871 A172060
Adjacent sequences: A119910 A119911 A119912 * A119914 A119915 A119916
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KEYWORD
| nonn
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AUTHOR
| Amir M. Ben-Amram (amirben(AT)mta.ac.il), Aug 02 2006
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Jan 18 2012
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