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Search: id:A003699
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| A003699 |
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Number of Hamilton cycles in C_4 X P_n. |
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+0
4
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| 1, 6, 22, 82, 306, 1142, 4262, 15906, 59362, 221542, 826806, 3085682, 11515922, 42978006, 160396102, 598606402, 2234029506, 8337511622, 31116016982, 116126556306, 433390208242, 1617434276662, 6036346898406
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
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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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n>1, a(n) = ceiling((1-sqrt(1/3))*(2+sqrt(3))^n); recurrence: a(1) = 1, a(2) = 6, a(3) = 22 and for n>3 a(n) = 4*a(n-1)-a(n-2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 28 2003
O.g.f.: -x*(-1-2*x+x^2)/(1-4*x+x^2) = -x-2+(-6*x+2)/(1-4*x+x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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CROSSREFS
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First differences of A052530 and A071954.
Equals 2 * A001835(n), n>1.
Sequence in context: A032195 A111566 A051945 this_sequence A047124 A046365 A078418
Adjacent sequences: A003696 A003697 A003698 this_sequence A003700 A003701 A003702
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KEYWORD
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nonn
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AUTHOR
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Frans Faase (Frans_LiXia(AT)wxs.nl)
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