login
Number of forests with no isolated vertices in Moebius ladder M_n.
1

%I #16 Aug 15 2015 16:54:04

%S 19,132,851,5298,32068,190711,1120947,6537903,37935984,219360837,

%T 1265462984,7288685420,41935203469,241094585397,1385405494499,

%U 7958227879396,45703889854759,262433722095008,1506738689157576,8650141792937245,49657618346464719

%N Number of forests with no isolated vertices in Moebius ladder M_n.

%H Colin Barker, <a href="/A020867/b020867.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_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-33,4,78,-39,-61,33,19,-10,-2,1).

%F G.f.: see G in the Maple program. - _Emeric Deutsch_, Dec 21 2004

%p G:=-(3*x^10-5*x^9-30*x^8+47*x^7+107*x^6-162*x^5-137*x^4+217*x^3+26*x^2-77*x+19)*x^2/(-1+6*x-x^2-3*x^3+x^4)/(1-4*x+x^3)/(-1+x+x^2)/(x^2-1): Gser:=series(G,x=0,25): seq(coeff(Gser,x^n),n=2..23); # _Emeric Deutsch_, Dec 21 2004

%o (PARI) Vec(-x^2*(3*x^10 -5*x^9 -30*x^8 +47*x^7 +107*x^6 -162*x^5 -137*x^4 +217*x^3 +26*x^2 -77*x +19) / ((x -1)*(x +1)*(x^2 +x -1)*(x^3 -4*x +1)*(x^4 -3*x^3 -x^2 +6*x -1)) + 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