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 A104221 #36 Feb 16 2025 08:32:56
%S A104221 0,0,0,2,2,4,8,12,20,34,54,88,144,232,376,610,986,1596,2584,4180,6764,
%T A104221 10946,17710,28656,46368,75024,121392,196418,317810,514228,832040,
%U A104221 1346268,2178308,3524578,5702886,9227464,14930352,24157816,39088168
%N A104221 a(n) = Fibonacci(n) - (Fibonacci(n) mod 2).
%C A104221 Also the circumference of the (n-2)-Fibonacci cube graph for n > 4. - _Eric W. Weisstein_, Sep 03 2017
%H A104221 Robert Israel, <a href="/A104221/b104221.txt">Table of n, a(n) for n = 0..4781</a>
%H A104221 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciCubeGraph.html">Fibonacci Cube Graph</a>.
%H A104221 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCircumference.html">Graph Circumference</a>.
%H A104221 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-1,-1).
%F A104221 a(n) = 2*A004695(n). - _R. J. Mathar_, Jul 23 2010
%F A104221 G.f.: 2*x^3/((1-x)*(1+x+x^2)*(1-x-x^2)). - _R. J. Mathar_, Jul 23 2010
%F A104221 a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) - a(n-5). - _Eric W. Weisstein_, Sep 03 2017
%F A104221 a(n) = Fibonacci(n) - A011655(n). - _David A. Corneth_, Mar 25 2018
%F A104221 a(n) = (1/3)*(-2 +3*Fibonacci(n) + 2*ChebyshevU(n, -1/2) + ChebyshevU(n-1, -1/2)). - _G. C. Greubel_, Jul 08 2022
%p A104221 f:= gfun:-rectoproc({a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) - a(n-5),
%p A104221 seq(a(i)=[0, 0, 0, 2, 2][i+1],i=0..4)},a(n),remember):
%p A104221 map(f, [$0..50]); # _Robert Israel_, Mar 25 2018
%t A104221 2*Floor[Fibonacci[Range[0, 50]]/2] (* _Eric W. Weisstein_, Sep 03 2017 *)
%t A104221 Table[2/3 (Cos[2n*Pi/3] -1) +Fibonacci[n], {n,0,50}] (* _Eric W. Weisstein_, Sep 03 2017 *)
%t A104221 Table[(I^n*LucasL[n,I] -2)/3 +Fibonacci[n], {n,0,50}] (* _Eric W. Weisstein_, Mar 25 2018 *)
%t A104221 LinearRecurrence[{1,1,1,-1,-1}, {0,0,0,2,2}, 51] (* _Eric W. Weisstein_, Sep 03 2017 *)
%t A104221 CoefficientList[Series[(2x^3)/(1-x-x^2-x^3+x^4+x^5), {x, 0, 20}], x] (* _Eric W. Weisstein_, Sep 03 2017 *)
%o A104221 (PARI) a(n) = 2*(fibonacci(n)\2); \\ _Altug Alkan_, Mar 25 2018
%o A104221 (Magma) [2*Floor(Fibonacci(n)/2): n in [0..40]]; // _G. C. Greubel_, Jul 08 2022
%o A104221 (SageMath) [2*(fibonacci(n)//2) for n in (0..40)] # _G. C. Greubel_, Jul 08 2022
%Y A104221 Cf. A000045, A004695, A011655, A049347.
%K A104221 nonn,easy
%O A104221 0,4
%A A104221 _Roger L. Bagula_, Mar 14 2005