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A003751
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Number of spanning trees in K_5 x P_n.
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1
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125, 300125, 663552000, 1464514260125, 3232184906328125, 7133430745792512000, 15743478429512478120125, 34745849760772636969860125, 76684074678559433693601792000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is a divisibility sequence.
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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. [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. [Paul Raff (paul(AT)myraff.com), Oct 29, 2009]
P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs. [Paul Raff (paul(AT)myraff.com), Oct 29, 2009]
Index to divisibility sequences
Index entries for sequences related to trees
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FORMULA
| a(n) = 2255a(n-1)- 105985a(n-2) +105985a(n-3) -2255a(n-4) +a(n-5).
a(n)=125*(A004187(n))^4 = 125*(A049682(n))^2. [R. Guy, seqfan list, Mar 28 2009] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]
G.f.: -(125x(x^3+146x^2+146x+1)/(x^5-2255x^4+105985x^3-105985x^2+2255x-1)) [Paul Raff (paul(AT)myraff.com), Oct 29, 2009]
a(n) = 125*F(4n)^4/81. - R. K. Guy, Feb 24 2010
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CROSSREFS
| Sequence in context: A030697 A050640 A161354 * A120807 A013836 A048563
Adjacent sequences: A003748 A003749 A003750 * A003752 A003753 A003754
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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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