This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A192810 #24 Mar 19 2025 07:21:36
%S A192810 0,1,5,23,109,527,2565,12503,60957,297183,1448821,7063207,34434061,
%T A192810 167870511,818390501,3989759863,19450597117,94824185471,462280211797,
%U A192810 2253676033863,10986963179245,53562871542735,261125950919109,1273022903354903
%N A192810 Coefficient of x^2 in the reduction of the polynomial (x^2 + 2)^n by x^3 -> x^2 + 2.
%C A192810 For discussions of polynomial reduction, see A192232 and A192744.
%H A192810 G. C. Greubel, <a href="/A192810/b192810.txt">Table of n, a(n) for n = 0..1000</a>
%H A192810 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-12,8).
%F A192810 a(n) = 7*a(n-1) - 12*a(n-2) + 8*a(n-3).
%F A192810 G.f.: x*(1-2*x)/(1-7*x+12*x^2-8*x^3). - _Colin Barker_, Jul 26 2012
%t A192810 (See A192808.)
%t A192810 LinearRecurrence[{7,-12,8}, {0,1,5}, 30] (* _G. C. Greubel_, Jan 02 2019 *)
%t A192810 CoefficientList[Series[x (1-2x)/(1-7x+12x^2-8x^3),{x,0,30}],x] (* _Harvey P. Dale_, Aug 26 2021 *)
%o A192810 (PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-2*x)/(1-7*x+12*x^2-8*x^3) )) \\ _G. C. Greubel_, Jan 02 2019
%o A192810 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1-2*x)/(1-7*x+12*x^2-8*x^3) )); // _G. C. Greubel_, Jan 02 2019
%o A192810 (Sage) (x*(1-2*x)/(1-7*x+12*x^2-8*x^3)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jan 02 2019
%o A192810 (GAP) a:=[0,1,5];; 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 A192810 Cf. A192744, A192232, A192808.
%K A192810 nonn,easy
%O A192810 0,3
%A A192810 _Clark Kimberling_, Jul 10 2011