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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

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), 129-154.

F. Faase, Counting Hamilton 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 6-term 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(n-1) - 1715a(n-2) + 4952a(n-3) - 1715a(n-4) + 140a(n-5) - a(n-6).

G.f.: 8x(1+4x-70x^2+4x^3+x^4)/((x^2-4x+1)(x^4-136x^3+1170x^2-136x+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

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Last modified November 20 00:42 EST 2017. Contains 294957 sequences.