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 A078024 #21 Sep 08 2022 08:45:08
%S A078024 1,-1,2,-1,3,0,5,3,10,11,23,32,57,87,146,231,379,608,989,1595,2586,
%T A078024 4179,6767,10944,17713,28655,46370,75023,121395,196416,317813,514227,
%U A078024 832042,1346267,2178311,3524576,5702889,9227463,14930354,24157815,39088171,63245984,102334157
%N A078024 Expansion of (1-x)/(1-2*x^2-x^3).
%H A078024 G. C. Greubel, <a href="/A078024/b078024.txt">Table of n, a(n) for n = 0..1000</a>
%H A078024 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1).
%F A078024 a(n) = Fibonacci(n+2) - Lucas(n) + 2*(-1)^n.
%F A078024 a(n) = (-1)^n*A112469(n). - _Philippe Deléham_, Apr 19 2013
%F A078024 a(n) = A008346(n) - A008346(n-1), n>=1. - _Philippe Deléham_, Apr 19 2013
%F A078024 a(n) = Fibonacci(n-2) + 2*(-1)^n. - _Philippe Deléham_, Apr 19 2013
%t A078024 LinearRecurrence[{0,2,1},{1,-1,2},50] (* _Harvey P. Dale_, Jan 14 2015 *)
%t A078024 Table[Fibonacci[n-2] +2*(-1)^n, {n,0,50}] (* _G. C. Greubel_, Aug 04 2019 *)
%o A078024 (PARI) Vec((1-x)/(1-2*x^2-x^3)+O(x^50)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A078024 (Magma) [Fibonacci(n-2) +2*(-1)^n: n in [0..50]]; // _G. C. Greubel_, Aug 04 2019
%o A078024 (Sage) [fibonacci(n-2) + 2*(-1)^n for n in (0..50)] # _G. C. Greubel_, Aug 04 2019
%o A078024 (GAP) List([0..50], n-> Fibonacci(n-2) + 2*(-1)^n); # _G. C. Greubel_, Aug 04 2019
%Y A078024 Cf. A000032, A000045, A008346, A112469.
%K A078024 sign,easy
%O A078024 0,3
%A A078024 _N. J. A. Sloane_, Nov 17 2002