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A003773
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Number of spanning trees in K_4 X P_n.
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1
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16, 3456, 686000, 135834624, 26894628304, 5325000912000, 1054323287943536, 208750686023540736, 41331581509440922000, 8183444388183674181504, 1620280657278860350213424, 320807386696826179092096000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| 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
| Paul Raff (praff(AT)math.rutgers.edu), Jun 04 2008, Table of n, a(n) for n = 1..15
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
Index entries for sequences related to trees
P. Raff, Spanning Trees in Grid Graphs. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]
P. Raff, Analysis of the Number of Spanning Trees of K_3 x P_n. Contains sequence, recurrence, generating function, and more. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]
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FORMULA
| a(1) = 16,
a(2) = 3456,
a(3) = 686000,
a(4) = 135834624,
a(5) = 26894628304 and
a(n) = 205a(n-1) - 1394a(n-2) + 1394a(n-3) - 205a(n-4) + a(n-5).
a(n) = 204*a(n-1) - 1190*a(n-2) + 204*a(n-3) - a(n-4). - Paul Raff (praff(AT)math.rutgers.edu), Jun 04 2008
G.f.: 16x(1+12x+x^2)/((1-6x+x^2)(x^2-198x+1)). a(n) = 35*A097731(n-1)/2 - 3*A001109(n)/2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 16 2008]
a(n)=16*(A001109(n))^3=16*A001109(n)*A001110(n). [R. Guy, seqfan list, Mar 28 2009] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]
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CROSSREFS
| Sequence in context: A091160 A049030 A051551 * A087519 A060616 A016936
Adjacent sequences: A003770 A003771 A003772 * A003774 A003775 A003776
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KEYWORD
| nonn
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AUTHOR
| Frans Faase (Frans_LiXia(AT)wxs.nl)
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EXTENSIONS
| More terms from Paul Raff (praff(AT)math.rutgers.edu), Jun 04 2008
Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009
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