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A003767
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Number of spanning trees in (K_4 - e) X P_n.
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0
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8, 1152, 147000, 18643968, 2363741512, 299675376000, 37992808932728, 4816723274883072, 610663532419269000, 77419840899743388288, 9815277065807118267832, 1244379512520754017408000
(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
| 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.
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_4 - e) x P_n. Contains sequence, recurrence, generating function, and more. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]
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
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FORMULA
| Faase gives a 6-term linear recurrence on his web page:
a(1) = 8,
a(2) = 1152,
a(3) = 147000,
a(4) = 18643968,
a(5) = 2363741512,
a(6) = 299675376000 and
a(n) = 140a(n-1) - 1715a(n-2) + 4952a(n-3) - 1715a(n-4) + 140a(n-5) - a(n-6).
G.f.: 8x(1+4x-70x^2+4x^3+x^4)/((x^2-4x+1)(x^4-136x^3+1170x^2-136x+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 16 2008]
a(n)=8*A001353(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: A176372 A047943 A089672 * A117084 A201985 A180767
Adjacent sequences: A003764 A003765 A003766 * A003768 A003769 A003770
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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
Title corrected by Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009
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