

A003767


Number of spanning trees in (K_4  e) X P_n.


0



8, 1152, 147000, 18643968, 2363741512, 299675376000, 37992808932728, 4816723274883072, 610663532419269000, 77419840899743388288, 9815277065807118267832, 1244379512520754017408000
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OFFSET

1,1


REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129154.


LINKS

Table of n, a(n) for n=1..12.
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), 129154.
F. Faase, Counting Hamiltonian cycles in product graphs
F. Faase, Results from the counting program
P. Raff, Spanning Trees in Grid Graphs.
P. Raff, Analysis of the Number of Spanning Trees of (K_4  e) x P_n. Contains sequence, recurrence, generating function, and more.
Index entries for sequences related to trees
Index entries for linear recurrences with constant coefficients, signature (140, 1715, 4952, 1715, 140, 1).


FORMULA

Faase gives a 6term linear recurrence on his web page:
a(1) = 8,
a(2) = 1152,
a(3) = 147000,
a(4) = 18643968,
a(5) = 2363741512,
a(6) = 299675376000 and
a(n) = 140a(n1)  1715a(n2) + 4952a(n3)  1715a(n4) + 140a(n5)  a(n6).
G.f.: 8x(1+4x70x^2+4x^3+x^4)/((x^24x+1)(x^4136x^3+1170x^2136x+1)). [From R. J. Mathar, Dec 16 2008]
a(n)=8*A001353(n)*A001110(n). [R. K. Guy, seqfan list, Mar 28 2009] [From R. J. Mathar, Jun 03 2009]


MATHEMATICA

LinearRecurrence[{140, 1715, 4952, 1715, 140, 1}, {8, 1152, 147000, 18643968, 2363741512, 299675376000}, 40] (* Harvey P. Dale, Mar 05 2013 *)


CROSSREFS

Sequence in context: A279881 A246114 A229164 * A221084 A117084 A201985
Adjacent sequences: A003764 A003765 A003766 * A003768 A003769 A003770


KEYWORD

nonn


AUTHOR

Frans J. Faase


EXTENSIONS

Added recurrence from Faase's web page.  N. J. A. Sloane, Feb 03 2009
Title corrected by Paul Raff, Mar 06 2009


STATUS

approved



