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A092136 Number of spanning trees in S_5 x P_n. 1
1, 189, 24576, 3046869, 375175625, 46151368704, 5676383392121, 698151521972709, 85867005969063936, 10560944392853518125, 1298910307853115410641, 159755407182415993503744 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

P. Raff, Analysis of the Number of Spanning Trees of S_5 x P_n. Contains sequence, recurrence, generating function, and more.

P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs.

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, 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, Jun 03 2009]

CROSSREFS

Sequence in context: A267993 A286791 A076012 * A259166 A156741 A138730

Adjacent sequences:  A092133 A092134 A092135 * A092137 A092138 A092139

KEYWORD

nonn

AUTHOR

Ralf Stephan, Mar 28 2004

STATUS

approved

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Last modified May 23 08:55 EDT 2017. Contains 286909 sequences.