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A092136
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Number of spanning trees in S_5 x P_n.
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1
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1, 189, 24576, 3046869, 375175625, 46151368704, 5676383392121, 698151521972709, 85867005969063936, 10560944392853518125, 1298910307853115410641, 159755407182415993503744
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| P. Raff, Table of n, a(n) for n = 1..200
F. Faase, Counting Hamilton cycles in product graphs
P. Raff, Spanning Trees in Grid Graphs. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 07 2009]
P. Raff, Analysis of the Number of Spanning Trees of S_5 x P_n. Contains sequence, recurrence, generating function, and more. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 07 2009]
P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs. [Added by Paul Raff (paul(AT)myraff.com), Oct 30 2009]
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FORMULA
| a(n) = 144 a(n-1)
- 2640 a(n-2)
+ 6930 a(n-3)
- 2640 a(n-4)
+ 144 a(n-5)
- a(n-6)
[Modified by Paul Raff (paul(AT)myraff.com), Oct 30, 2009]
G.f.: -x(x^4+45x^3-45x-1)/(x^6-144x^5+2640x^4-6930x^3+2640x^2-144x+1) [From Paul Raff (paul(AT)myraff.com, Mar 07 2009]
a(n)=A004187(n)*(A001906(n))^3 = A004187(n)*A001906(n)*A049684(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: A178228 A133351 A076012 * A156741 A138730 A159821
Adjacent sequences: A092133 A092134 A092135 * A092137 A092138 A092139
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan, Mar 28 2004
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