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 A003761 Number of spanning trees in D_4 X P_n. 1
 3, 270, 20160, 1477980, 108097935, 7903526400, 577834413429, 42245731959480, 3088601154192960, 225808743709815750, 16508958287605688193, 1206975861055570636800, 88242438021480689844999, 6451436286916714206370530, 471666820375043557337304000 (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 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. [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 a(n) = 3*A006238(n)*A001109(n). [R. Guy, seqfan list, Mar 28 2009] - R. J. Mathar, Jun 03 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 Sequence in context: A219550 A058451 A230373 * A216471 A223037 A171358 Adjacent sequences:  A003758 A003759 A003760 * A003762 A003763 A003764 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

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