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A192907 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.

%I A192907 #14 Sep 08 2022 08:45:58
%S A192907 0,1,4,12,37,116,364,1141,3576,11208,35129,110104,345096,1081625,
%T A192907 3390108,10625524,33303293,104381612,327160468,1025410221,3213915568,
%U A192907 10073288784,31572437041,98956636912
%N A192907 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
%C A192907 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 + 1.
%H A192907 G. C. Greubel, <a href="/A192907/b192907.txt">Table of n, a(n) for n = 0..1000</a>
%H A192907 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,1,1).
%F A192907 a(n) = 3*a(n-1) + a(n-3) + a(n-4).
%F A192907 G.f. x*(1+x)/( 1-3*x-x^3-x^4 ). - _R. J. Mathar_, Jul 13 2011
%t A192907 (See A192906.)
%t A192907 LinearRecurrence[{3,0,1,1}, {0,1,4,12}, 30] (* _G. C. Greubel_, Jan 11 2019 *)
%o A192907 (PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1+x)/(1-3*x-x^3-x^4))) \\ _G. C. Greubel_, Jan 11 2019
%o A192907 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1+x)/(1-3*x-x^3-x^4) )); // _G. C. Greubel_, Jan 11 2019
%o A192907 (Sage) (x*(1+x)/(1-3*x-x^3-x^4)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jan 11 2019
%o A192907 (GAP) a:=[0,1,4,12];; 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 A192907 Cf. A192906.
%K A192907 nonn
%O A192907 0,3
%A A192907 _Clark Kimberling_, Jul 12 2011