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
Sean A. Irvine, Table of n, a(n) for n = 1..100
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, Results from the counting program
P. Raff, Spanning Trees in Grid Graphs, arXiv:0809.2551 [math.CO], 2008. [From Paul Raff, Mar 06 2009]
P. Raff, Analysis of the Number of Spanning Trees of D_4 x P_n. Contains sequence, recurrence, generating function, and more. [From Paul Raff, Mar 06 2009]
Index entries for linear recurrences with constant coefficients, signature (90,-1313,5850,-9828,5850,-1313,90,-1).
FORMULA
a(1) = 3,
a(2) = 270,
a(3) = 20160,
a(4) = 1477980,
a(5) = 108097935,
a(6) = 7903526400,
a(7) = 577834413429,
a(8) = 42245731959480 and
a(n) = 90*a(n-1) - 1313*a(n-2) + 5850*a(n-3) - 9828*a(n-4) + 5850*a(n-5) - 1313*a(n-6) + 90*a(n-7) - a(n-8).
G.f.: 3*x*(x^6 -67*x^4 +180*x^3 -67*x^2 +1) / (x^8 -90*x^7 +1313*x^6 -5850*x^5 +9828*x^4 -5850*x^3 +1313*x^2 -90*x +1). - Paul Raff, Mar 06 2009
MATHEMATICA
CoefficientList[Series[3 (x^6 - 67 x^4 + 180 x^3 - 67 x^2 + 1)/(x^8 - 90 x^7 + 1313 x^6 - 5850 x^5 + 9828 x^4 - 5850 x^3 + 1313 x^2 - 90 x + 1), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 03 2015 *)
PROG
(Magma) I:=[3, 270, 20160, 1477980, 108097935, 7903526400, 577834413429, 42245731959480]; [n le 8 select I[n] else 90*Self(n-1)-1313*Self(n-2)+5850*Self(n-3)-9828*Self(n-4)+5850*Self(n-5)-1313*Self(n-6)+90*Self(n-7)-Self(n-8): n in [1..20]]; // Vincenzo Librandi, Aug 03 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Recurrence from Faase's web page added by N. J. A. Sloane, Feb 03 2009
More terms from Sean A. Irvine, Aug 02 2015
STATUS
approved