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A192923 Coefficient of x in the reduction by (x^2->x+1) of the polynomial p(n,x) defined below at Comments.

%I A192923 #17 Sep 08 2022 08:45:58
%S A192923 0,1,2,4,9,19,42,91,200,437,959,2101,4609,10106,22168,48620,106649,
%T A192923 233928,513126,1125541,2468901,5415578,11879209,26057330,57157443,
%U A192923 125376341,275016369,603255761
%N A192923 Coefficient of x in the reduction by (x^2->x+1) of the polynomial p(n,x) defined below at Comments.
%C A192923 The titular polynomial is defined by p(n,x) = p(n-1,x) +(x^2)*p(n-2,x), with p(0,x)=1, p(1,x)=x.  For discussions of polynomial reduction, see A192232, A192744, and A192872.
%H A192923 G. C. Greubel, <a href="/A192923/b192923.txt">Table of n, a(n) for n = 0..1000</a>
%H A192923 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-3,-1).
%F A192923 a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3) - a(n-4).
%F A192923 G.f.: x*(1-2*x^2) / ( 1-2*x-2*x^2+3*x^3+x^4 ). - _R. J. Mathar_, May 08 2014
%t A192923 (See A192922.)
%t A192923 CoefficientList[Series[x*(1-2*x^2)/(1-2*x-2*x^2+3*x^3+x^4), {x, 0, 30}], x] (* _G. C. Greubel_, Jun 26 2017 *)
%o A192923 (PARI) x='x+O('x^30); concat([0], Vec(x*(1-2*x^2)/(1-2*x-2*x^2+3*x^3+x^4) )) \\ _G. C. Greubel_, Jun 26 2017
%o A192923 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1-2*x^2)/(1-2*x-2*x^2+3*x^3+x^4) )); // _G. C. Greubel_, Feb 06 2019
%o A192923 (Sage) (x*(1-2*x^2)/(1-2*x-2*x^2+3*x^3+x^4)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Feb 06 2019
%o A192923 (GAP) a:=[0,1,2,4];; for n in [5..30] do a[n]:=2*a[n-1]+2*a[n-2]-3*a[n-3] -a[n-4]; od; a; # _G. C. Greubel_, Feb 06 2019
%Y A192923 Cf. A192232, A192744, A192922.
%K A192923 nonn
%O A192923 0,3
%A A192923 _Clark Kimberling_, Jul 12 2011