%I #23 Jun 07 2024 18:51:16

%S 1,3,15,66,300,1353,6114,27615,124743,563475,2545284,11497332,

%T 51934755,234595164,1059692925,4786752927,21622304991,97670399970,

%U 441188256072,1992897309225,9002142805206,40663698380283,183682530009075,829714786761531,3747915641932500

%N Expansion of ( 1-x ) / ( 1-4*x-3*x^2+3*x^3 ).

%H Vincenzo Librandi, <a href="/A052981/b052981.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1054">Encyclopedia of Combinatorial Structures 1054</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,3,-3)

%F G.f.: (1-x)/(1-4*x-3*x^2+3*x^3).

%F Recurrence: {a(0)=1, a(1)=3, a(2)=15, 3*a(n)-3*a(n+1)-4*a(n+2)+a(n+3)=0}.

%F Sum(-1/95*(-11-22*r+15*r^2)*r^(-1-n) where r=RootOf(1-4*_Z-3*_Z^2+3*_Z^3)).

%p spec:= [S, {S=Sequence(Prod(Union(Z,Z,Z), Union(Sequence(Z),Z)))}, unlabeled]: seq(combstruct[count ](spec, size=n), n=0..20);

%t LinearRecurrence[{4,3,-3},{1,3,15},40] (* _Vincenzo Librandi_, Jun 23 2012 *)

%t CoefficientList[Series[(1-x)/(1-4x-3x^2+3x^3),{x,0,30}],x] (* _Harvey P. Dale_, Jun 07 2024 *)

%o (Magma) I:=[1, 3, 15]; [n le 3 select I[n] else 4*Self(n-1)+3*Self(n-2) -3*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 23 2012

%K easy,nonn

%O 0,2

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000