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Search: id:A006864
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| A006864 |
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Number of Hamilton cycles in P_4 X P_n.
(Formerly M1603)
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+0
2
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| 0, 1, 2, 6, 14, 37, 92, 236, 596, 1517, 3846, 9770, 24794, 62953, 159800, 405688, 1029864, 2614457, 6637066, 16849006, 42773094, 108584525, 275654292, 699780452, 1776473532, 4509783909, 11448608270, 29063617746
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
Kwong, Y. H. H.; Enumeration of Hamiltonian cycles in $P\sb 4\times P\sb n$ and $P\sb 5\times P\sb n$. Ars Combin. 33 (1992), 87-96.
Tosic R., Bodroza O., Harris Kwong Y. H. and Joseph Straight H., On the number of Hamiltonian cycles of P4 X Pn, Indian J. Pure Appl. Math. 21 (5) (1990), 403-409.
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LINKS
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F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
F. Faase, Counting Hamilton cycles in product graphs
F. Faase, Results from the counting program
F. Faase, Counting Hamilton cycles in product graphs
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FORMULA
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a(n) = 2a(n-1) + 2a(n-2) - 2a(n-3) + a(n-4).
G.f.: x^2/(1-2x-2x^2+2x^3-x^4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 16 2008]
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CROSSREFS
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Sequence in context: A006653 A144530 A026598 this_sequence A071636 A100067 A026597
Adjacent sequences: A006861 A006862 A006863 this_sequence A006865 A006866 A006867
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KEYWORD
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easy,nonn
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AUTHOR
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kwong(AT)cs.fredonia.edu (Harris Kwong), N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe and Frans Faase (Frans_LiXia(AT)wxs.nl)
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