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A192905 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.

%I A192905 #15 Sep 08 2022 08:45:58
%S A192905 0,1,3,8,25,79,248,777,2435,7632,23921,74975,234992,736529,2308483,
%T A192905 7235416,22677769,71078319,222778856,698249753,2188505347,6859373216,
%U A192905 21499148257,67384199871,211200478176,661959956001,2074763216131
%N A192905 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
%C A192905 The titular polynomial is defined by p(n,x) = (x^2)*p(n-1,x) + x*p(n-2,x), with p(0,x) = 1, p(1,x) = x.  For details, see A192904.
%H A192905 G. C. Greubel, <a href="/A192905/b192905.txt">Table of n, a(n) for n = 0..1000</a>
%H A192905 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,1,1).
%F A192905 a(n) = 3*a(n-1) + a(n-3) + a(n-4).
%F A192905 G.f.: x*(1-x)*(1+x)/(1-3*x-x^3-x^4). - _Colin Barker_, Aug 31 2012
%t A192905 (See A192904.)
%t A192905 LinearRecurrence[{3,0,1,1}, {0,1,3,8}, 30] (* _G. C. Greubel_, Jan 11 2019 *)
%o A192905 (PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-x^2)/(1-3*x-x^3-x^4))) \\ _G. C. Greubel_, Jan 11 2019
%o A192905 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1-x^2)/(1-3*x-x^3-x^4) )); // _G. C. Greubel_, Jan 11 2019
%o A192905 (Sage) (x*(1-x^2)/(1-3*x-x^3-x^4)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jan 11 2019
%o A192905 (GAP) a:=[0,1,3,8];; for n in [5..30] do a[n]:=3*a[n-1]+a[n-3]+a[n-4]; od; a; # _G. C. Greubel_, Jan 11 2019
%Y A192905 Cf. A192232, A192744, A192904, A192872.
%K A192905 nonn,easy
%O A192905 0,3
%A A192905 _Clark Kimberling_, Jul 12 2011