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 A165206 #13 Dec 16 2024 05:27:50
%S A165206 1,-3,-25,-112,-416,-1411,-4537,-14085,-42653,-126794,-371554,
%T A165206 -1076423,-3089555,-8799207,-24897121,-70052356,-196151492,-546916555,
%U A165206 -1519249933,-4206274089,-11611243109,-31967026718,-87796880710
%N A165206 a(n) = (3-4*n)*F(2*n-2) + (4-7*n)*F(2*n-1).
%C A165206 Hankel transform of A165205.
%H A165206 G. C. Greubel, <a href="/A165206/b165206.txt">Table of n, a(n) for n = 0..1000</a>
%H A165206 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6,-1).
%F A165206 G.f.: (1-9*x+4*x^2-x^3)/(1-3*x+x^2)^2 = (1-x)/(1-3*x+x^2) - 5*x/(1-3*x+x^2)^2.
%F A165206 a(n) = -5*A001871(n-1) + A001519(n+1). - _R. J. Mathar_, Dec 16 2024
%t A165206 Table[(3-4n)Fibonacci[2n-2]+(4-7n)Fibonacci[2n-1],{n,0,30}] (* or *) LinearRecurrence[{6,-11,6,-1},{1,-3,-25,-112},30] (* _Harvey P. Dale_, Aug 25 2013 *)
%o A165206 (PARI) vector(30, n, n--; f=fibonacci; (3-4*n)*f(2*n-2)+(4-7*n)*f(2*n-1)) \\ _G. C. Greubel_, Jul 18 2019
%o A165206 (Magma) F:=Fibonacci; [(3-4*n)*F(2*n-2)+(4-7*n)*F(2*n-1): n in [0..30]]; // _G. C. Greubel_, Jul 18 2019
%o A165206 (Sage) f=fibonacci; [(3-4*n)*f(2*n-2)+(4-7*n)*f(2*n-1) for n in (0..30)] # _G. C. Greubel_, Jul 18 2019
%o A165206 (GAP) F:=Fibonacci;; List([0..30], n-> (3-4*n)*F(2*n-2)+(4-7*n)*F(2*n-1) ); # _G. C. Greubel_, Jul 18 2019
%Y A165206 Cf. A000045.
%K A165206 easy,sign
%O A165206 0,2
%A A165206 _Paul Barry_, Sep 07 2009