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A003690
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Number of spanning trees in K_3 X P_n.
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6
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3, 75, 1728, 39675, 910803, 20908800, 479991603, 11018898075, 252954664128, 5806938376875, 133306628004003, 3060245505715200, 70252340003445603, 1612743574573533675, 37022849875187828928
(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.
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(n) = 24a(n-1) - 24a(n-2) + a(n-3), n>3.
G.f.: 3x(1+x)/((1-x)(1-23x+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 16 2008]
a(n)=3*(A004254(n))^2. [R. Guy, seqfan list, Mar 28 2009] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]
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CROSSREFS
| Equals (A090731(n)-2)/7.
Sequence in context: A060869 A012491 A136328 * A195263 A034940 A183290
Adjacent sequences: A003687 A003688 A003689 * A003691 A003692 A003693
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KEYWORD
| nonn
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AUTHOR
| Frans Faase (Frans_LiXia(AT)wxs.nl)
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