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A003733
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Number of spanning trees in C_5 X P_n.
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7
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5, 1805, 508805, 140503005, 38720000000, 10668237057005, 2939274449134805, 809816405722655805, 223117116976138566005, 61472262298219520000000, 16936571572967914651674005
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) = 5 * (A143699(n))^2. - R. K. Guy, Mar 11 2010
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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, arXiv:0809.2551. [Added by Paul Raff, Oct 30 2009]
P. Raff, Analysis of the Number of Spanning Trees of C_5 x P_n. Contains sequence, recurrence, generating function, and more. [Added by Paul Raff, Oct 30 2009]
P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs. [Added by Paul Raff, Oct 30 2009]
Index entries for sequences related to trees
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FORMULA
| a(n) = 319 a(n-1)
- 12441 a(n-2)
+ 128319 a(n-3)
- 408001 a(n-4)
+ 408001 a(n-5)
- 128319 a(n-6)
+ 12441 a(n-7)
- 319 a(n-8)
+ a(n-9).
[Modified by Paul Raff, Oct 30, 2009]
G.f.: -5*x *(1+x) *(x^6+41*x^5-998*x^4+2722*x^3-998*x^2+41*x+1) / ( (x-1)*(x^4-279*x^3+961*x^2-279*x+1) *(x^4-39*x^3+281*x^2-39*x+1) ).
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MAPLE
| a:= n-> (Matrix(1, 9, (i, j)-> [0, 5, 1805, 508805, 140503005][1+abs(j-5)]). Matrix(9, (i, j)-> if (i=j-1) then 1 elif j=1 then -[408001, 128319, 12441, 319, 1][1/2+abs(i-9/2)] *(-1)^i else 0 fi)^n)[1, 5]: seq (a(n), n=1..20); # Alois P. Heinz, Mar 28 2009
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CROSSREFS
| Cf. A143699.
Sequence in context: A198246 A122465 A203683 * A201300 A024073 A105035
Adjacent sequences: A003730 A003731 A003732 * A003734 A003735 A003736
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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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