%I #21 Apr 18 2017 07:04:21
%S 0,2,2,6,12,28,62,140,314,706,1586,3564,8008,17994,40432,90850,204138,
%T 458694,1030676,2315908,5203798,11692828,26273546,59036122,132652962,
%U 298068500,669753840,1504923218,3381531776,7598232930,17073074418
%N Expansion of 2x(1-x)/(1-2x-x^2+x^3).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1071">Encyclopedia of Combinatorial Structures 1071</a>
%H Sergey Kitaev, Jeffrey Remmel, <a href="http://arxiv.org/abs/1304.4286">(a,b)-rectangle patterns in permutations and words</a>, arXiv:1304.4286 [math.CO], 2013.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-1).
%F G.f.: -2*x*(-1+x)/(x^3-x^2-2*x+1)
%F Recurrence: {a(0)=0, a(1)=2, a(2)=2, a(n)-a(n+1)-2*a(n+2)+a(n+3)=0}
%F Sum(2/7*(-_alpha+_alpha^2+1)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))
%p spec := [S,{S=Prod(Sequence(Prod(Union(Sequence(Z),Z),Z)),Union(Z,Z))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%o (PARI) concat(0, Vec(-2*x*(-1+x)/(x^3-x^2-2*x+1) + O(x^40))) \\ _Michel Marcus_, Mar 19 2015
%Y Equals 2 * A006356(n-2), n>1.
%K easy,nonn
%O 0,2
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E More terms from _James A. Sellers_, Jun 05 2000