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Search: id:A003761
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| A003761 |
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Number of spanning trees in D_4 X P_n. |
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1
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| 3, 270, 20160, 1477980, 108097935, 7903526400, 577834413429, 42245731959480, 3088601154192960, 225808743709815750, 16508958287605688193, 1206975861055570636800
(list; graph; listen)
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OFFSET
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1,1
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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
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 D_4 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
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a(1) = 3,
a(2) = 270,
a(3) = 20160,
a(4) = 1477980,
a(5) = 108097935,
a(6) = 7903526400,
a(7) = 577834413429,
a(8) = 42245731959480 and
a(n) = 90a(n-1) - 1313a(n-2) + 5850a(n-3) - 9828a(n-4) + 5850a(n-5) - 1313a(n-6) + 90a(n-7) - a(n-8).
G.f.: 3x(x^6-67x^4+180x^3-67x^2+1)/(x^8-90x^7+1313x^6-5850x^5+9828x^4-5850x^3+1313x^2-90x+1) [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]
a(n)=3*A006238(n)*A001109(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
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Sequence in context: A051490 A003381 A058451 this_sequence A105318 A115477 A051365
Adjacent sequences: A003758 A003759 A003760 this_sequence A003762 A003763 A003764
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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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EXTENSIONS
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Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009
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