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%I A052546 #26 Sep 08 2022 08:44:59
%S A052546 1,0,1,3,2,7,13,18,41,71,122,239,421,762,1417,2543,4642,8495,15389,
%T A052546 28082,51177,93047,169610,308847,562197,1024170,1864841,3395711,
%U A052546 6184498,11261551,20507789,37346914,68008809,123848199,225535258
%N A052546 Expansion of (1-x)/(1-x-x^2-2*x^3+2*x^4).
%H A052546 G. C. Greubel, Table of n, a(n) for n = 0..1000
%H A052546 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 482
%H A052546 Index entries for linear recurrences with constant coefficients, signature (1,1,2,-2).
%F A052546 G.f.: (1-x)/(1-x-2*x^3+2*x^4-x^2).
%F A052546 a(n) = a(n-1) + a(n-2) + 2*a(n-3) - 2*a(n-4), with a(0)=1, a(1)=0, a(2)=1, a(3)=3.
%F A052546 a(n) = Sum_{alpha = RootOf(1-x-2*x^3+2*x^4-x^2)} (-1/353 * (-18-106*alpha+33*alpha^2+28*alpha^3) * alpha^(-1-n)).
%p A052546 spec := [S,{S=Sequence(Prod(Z,Z,Union(Z,Z,Sequence(Z))))},unlabeled]: seq(combstruct[count](spec,size=n), n=0..40);
%t A052546 CoefficientList[Series[(1-x)/(1-x-x^2-2x^3+2x^4),{x,0,40}],x] (* or *) LinearRecurrence[{1,1,2,-2},{1,0,1,3},40] (* _Harvey P. Dale_, Jul 02 2017 *)
%o A052546 (PARI) my(x='x+O('x^40)); Vec((1-x)/(1-x-2*x^3+2*x^4-x^2)) \\ _G. C. Greubel_, May 08 2019
%o A052546 (Magma) R