A192809 - OEIS

%I #19 Sep 08 2022 08:45:58

%S 0,0,2,14,74,366,1786,8702,42410,206734,1007834,4913310,23953034,

%T 116774190,569289402,2775359806,13530239338,65961672910,321571716762,

%U 1567703857118,7642759781962,37259445922414,181644634930298,885541171698814

%N Coefficient of x in the reduction of the polynomial (x^2 + 2)^n by x^3 -> x^2 + 2.

%C For discussions of polynomial reduction, see A192232 and A192744.

%H G. C. Greubel, <a href="/A192809/b192809.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-12,8).

%F a(n) = 7*a(n-1) - 12*a(n-2) + 8*a(n-3).

%F a(n) = 2*A192811(n).

%F G.f.: 2*x^2/(1-7*x+12*x^2-8*x^3). - _Colin Barker_, Jul 26 2012

%t (See A192808.)

%t LinearRecurrence[{7,-12,8}, {0,0,2}, 30] (* _G. C. Greubel_, Jan 02 2019 *)

%o (PARI) my(x='x+O('x^30)); concat([0,0], Vec(2*x^2/(1-7*x+12*x^2-8*x^3))) \\ _G. C. Greubel_, Jan 02 2019

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0,0] cat Coefficients(R!( 2*x^2/(1-7*x+12*x^2-8*x^3) )); // _G. C. Greubel_, Jan 02 2019

%o (Sage) (2*x^2/(1-7*x+12*x^2-8*x^3)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jan 02 2019

%o (GAP) a:=[0,0,2];; for n in [4..25] do a[n]:=7*a[n-1]-12*a[n-2]+8*a[n-3]; od; Print(a); # _Muniru A Asiru_, Jan 02 2019

%Y Cf. A192744, A192232, A192808, A192811.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Jul 10 2011