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A003745
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Number of spanning trees in (K_5 - e) x P_n.
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1
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75, 128625, 199065600, 307147367625, 473862674071875, 731065883885568000, 1127873690900648512275, 1740060755637940344737625, 2684530596730102104276172800
(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
| P. Raff, Table of n, a(n) for n = 1..200
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
P. Raff, Spanning Trees in Grid Graphs. [Added by Paul Raff (paul(AT)myraff.com, Oct 29, 2009]
P. Raff, Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}}. Contains sequence, recurrence, generating function, and more. [Added by Paul Raff (paul(AT)myraff.com, Oct 29, 2009]
P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs. [Added by Paul Raff (paul(AT)myraff.com, Oct 29, 2009]
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FORMULA
| a(n) = 1645 a(n-1)
- 160129 a(n-2)
+ 3747310 a(n-3)
- 7579606 a(n-4)
+ 3747310 a(n-5)
- 160129 a(n-6)
+ 1645 a(n-7)
- a(n-8)
[Modified by Paul Raff (paul(AT)myraff.com), Oct 29, 2009]
G.f.: -75x(x^6+70x^5-6838x^4+6838x^2-70x-1)/(x^8-1645x^7+160129x^6-3747310x^5+7579606x^4-3747310x^3+160129x^2-1645x+1) [Paul Raff (paul(AT)myraff.com), Oct 29, 2009]
a(n)=75*A001906(n)*(A004187(n))^3. [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: A116527 A085404 A110100 * A068942 A116234 A065669
Adjacent sequences: A003742 A003743 A003744 * A003746 A003747 A003748
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KEYWORD
| nonn
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AUTHOR
| Frans Faase (Frans_LiXia(AT)wxs.nl)
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EXTENSIONS
| Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009
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