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 A075150 #17 Jun 16 2025 00:41:59
%S A075150 4,-1,9,-16,49,-121,324,-841,2209,-5776,15129,-39601,103684,-271441,
%T A075150 710649,-1860496,4870849,-12752041,33385284,-87403801,228826129,
%U A075150 -599074576,1568397609,-4106118241,10749957124,-28143753121,73681302249,-192900153616,505019158609,-1322157322201
%N A075150 a(n) = L(n)*C(n), L(n)=Lucas numbers (A000032), C(n)=reflected Lucas numbers (see comment to A061084).
%H A075150 Colin Barker, <a href="/A075150/b075150.txt">Table of n, a(n) for n = 0..1000</a>
%H A075150 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,2,1).
%F A075150 a(n) = (-1)^n*A000032(2*n) + 2.
%F A075150 a(n) = -2*a(n-1) + 2*a(n-2) + a(n-3) with a(0)=4, a(1)=-1, a(2)=9.
%F A075150 G.f.: (4 + 7*x - x^2)/(1 + 2*x - 2*x^2 - x^3).
%F A075150 a(n) = (-1)^n*A001254(n). - _R. J. Mathar_, Jan 11 2012
%F A075150 a(n) = 2 + (1/2*(-3-sqrt(5)))^n + (1/2*(-3+sqrt(5)))^n. - _Colin Barker_, Oct 01 2016
%F A075150 From _G. C. Greubel_, Jun 14 2025: (Start)
%F A075150 a(n) = A000032(n)*A000032(-n) = (-1)^n*A000032(n)^2.
%F A075150 a(n) = A219233(n) + 2 + [n=0].
%F A075150 E.g.f.: 2*exp(-3*x/2)*cosh(sqrt(5)*x/2) + 2*exp(x). (End)
%t A075150 CoefficientList[Series[(4 + 7*x - x^2)/(1 + 2*x - 2*x^2 - x^3), {x, 0, 30}], x]
%t A075150 LinearRecurrence[{-2,2,1},{4,-1,9},50] (* _Harvey P. Dale_, Nov 08 2011 *)
%o A075150 (PARI) a(n) = round((2+(1/2*(-3-sqrt(5)))^n+(1/2*(-3+sqrt(5)))^n)) \\ _Colin Barker_, Oct 01 2016
%o A075150 (PARI) Vec((4+7*x-x^2)/(1+2*x-2*x^2-x^3) + O(x^30)) \\ _Colin Barker_, Oct 01 2016
%o A075150 (Magma)
%o A075150 A075150:= func< n | (-1)^n*Lucas(n)^2 >; // _G. C. Greubel_, Jun 14 2025
%o A075150 (SageMath)
%o A075150 def A075150(n): return (-1)**n*lucas_number2(n,1,-1)**2 # _G. C. Greubel_, Jun 14 2025
%Y A075150 Cf. A000032, A001254, A061084, A219233.
%K A075150 easy,sign
%O A075150 0,1
%A A075150 Mario Catalani (mario.catalani(AT)unito.it), Sep 05 2002