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Expansion of 2x(1-x)/(1-2x-x^2+x^3).
2

%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