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A112849
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Number of congruence classes (epimorphisms/vertex partitionings induced by graph endomorphisms) of undirected cycles of even length: |C(C_2n)|.
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2
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1, 4, 11, 36, 127, 463, 1717, 6436, 24311, 92379, 352717, 1352079, 5200301, 20058301, 77558761, 300540196, 1166803111, 4537567651, 17672631901, 68923264411, 269128937221, 1052049481861, 4116715363801, 16123801841551, 63205303218877, 247959266474053, 973469712824057, 3824345300380221, 15033633249770521
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| M. A. Michels, About The Structure of Graph Endomorphisms, Diploma thesis, University of Oldenburg, Germany, 2005
M. A. Michels and U. Knauer, The congruence classes of paths and cycles, Discrete Math., 309 (2009), 5352-5359. [From N. J. A. Sloane, Sep 15 2009]
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
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FORMULA
| |C(C_2n)| = 1 + (1/2)*binomial(2n-1, n-1) + (1/2)*binomial(2n-1, n), n>1.
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MAPLE
| egf := n->exp(exp(x)*(1-(GAMMA(n, x)/GAMMA(n)))):
a := n->`if`(n=1, 1, (2*n)!*coeff(series(egf(n), x, 2*n+1), x, 2*n)):
seq(a(n), n=1..29); - Peter Luschny, Apr 05 2011.
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CROSSREFS
| Cf. A112850.
Sequence in context: A149241 A149242 A149243 * A149244 A149245 A054105
Adjacent sequences: A112846 A112847 A112848 * A112850 A112851 A112852
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KEYWORD
| easy,nonn
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AUTHOR
| Martin Alexander Michels (martinmichels(AT)t-online.de), Sep 24 2005
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