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Number of single component forests in Moebius ladder M_n.
1

%I #20 May 17 2019 02:35:36

%S 34,222,1280,6955,36378,185178,923696,4535991,22000490,105640634,

%T 503067648,2379006071,11183747330,52306745310,243553038816,

%U 1129612848795,5221079904978,24057393297286,110543216068160,506673892786803,2317069421129034,10574292843014802

%N Number of single component forests in Moebius ladder M_n.

%H Colin Barker, <a href="/A020869/b020869.txt">Table of n, a(n) for n = 2..1000</a>

%H J. P. McSorley, <a href="http://dx.doi.org/10.1016/S0012-365X(97)00086-1">Counting structures in the Moebius ladder</a>, Discrete Math., 184 (1998), 137-164.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (13,-64,156,-218,190,-108,40,-9,1).

%F G.f.: x^2*(3x^8 - 27x^7 + 126x^6 - 360x^5 + 663x^4 - 781x^3 + 570x^2 - 220x + 34)/((1-x)^3*(1 - 5x + 3x^2 - x^3)^2). - _Emeric Deutsch_, Dec 21 2004

%F The McSorley reference gives the approximation a(n) ~ 0.8757*n*4.3652^n - 1.5432*n*0.4786^n*cos(0.8458*n+0.9674) + n^2 - 2*n. - _Emeric Deutsch_, Dec 21 2004

%p G:=x^2*(3*x^8-27*x^7+126*x^6-360*x^5+663*x^4-781*x^3+570*x^2-220*x+34)/(1-x)^3/(1-5*x+3*x^2-x^3)^2: Gser:=series(G,x=0,27): seq(coeff(Gser,x^n),n=2..25); # _Emeric Deutsch_, Dec 21 2004

%o (PARI) Vec(-x^2*(3*x^8-27*x^7+126*x^6-360*x^5+663*x^4-781*x^3+570*x^2-220*x+34) / ((x-1)^3*(x^3-3*x^2+5*x-1)^2) + O(x^30)) \\ _Colin Barker_, Aug 01 2015

%K nonn,easy

%O 2,1

%A _N. J. A. Sloane_

%E More terms from _Emeric Deutsch_, Dec 21 2004