The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003733 Number of spanning trees in C_5 X P_n. 8
 5, 1805, 508805, 140503005, 38720000000, 10668237057005, 2939274449134805, 809816405722655805, 223117116976138566005, 61472262298219520000000, 16936571572967914651674005, 4666290873812984282155907805, 1285636259054921313298518442805 (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 P. Raff, Table of n, a(n) for n = 1..200 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. [Added by Paul Raff, Oct 30 2009] P. Raff, Analysis of the Number of Spanning Trees of C_5 x P_n. Contains sequence, recurrence, generating function, and more. [Added by Paul Raff, Oct 30 2009] [broken link] P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs. [Added by Paul Raff, Oct 30 2009]  [broken link] Index entries for linear recurrences with constant coefficients, signature (319, -12441, 128319, -408001, 408801, -128319, 12441, -319, 1). FORMULA a(n) = 319*a(n-1) - 12441*a(n-2) + 128319*a(n-3) - 408001*a(n-4) + 408001*a(n-5) - 128319*a(n-6) + 12441*a(n-7) - 319*a(n-8) + a(n-9). [Modified by Paul Raff, Oct 30 2009] G.f.: -5*x *(1+x) *(x^6+41*x^5-998*x^4+2722*x^3-998*x^2+41*x+1) / ( (x-1)*(x^4-279*x^3+961*x^2-279*x+1) *(x^4-39*x^3+281*x^2-39*x+1) ). a(n) = 5 * (A143699(n))^2. - R. K. Guy, Mar 11 2010 MAPLE a:= n-> (Matrix(1, 9, (i, j)-> [0, 5, 1805, 508805, 140503005][1+abs(j-5)]). Matrix(9, (i, j)-> if (i=j-1) then 1 elif j=1 then -[408001, 128319, 12441, 319, 1][1/2+abs(i-9/2)] *(-1)^i else 0 fi)^n)[1, 5]: seq(a(n), n=1..20); # Alois P. Heinz, Mar 28 2009 MATHEMATICA a[n_] := (16/41)*Sinh[n*ArcCosh[(-9 - Sqrt)/4]]^2*Sinh[n*ArcCosh[(-9 + Sqrt)/4]]^2 // Round; Array[a, 20] (* Jean-François Alcover, Jan 31 2016, after Peter Bala in A143699 *) CROSSREFS Cf. A143699. Sequence in context: A203683 A330057 A324265 * A201300 A024073 A301532 Adjacent sequences:  A003730 A003731 A003732 * A003734 A003735 A003736 KEYWORD nonn AUTHOR EXTENSIONS Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 27 09:48 EDT 2022. Contains 357054 sequences. (Running on oeis4.)