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 A099505 #11 Aug 04 2023 01:44:23
%S A099505 0,1,1,2,1,2,0,1,-3,-2,-8,-5,-12,-4,-11,6,-1,28,16,56,26,72,3,51,-80,
%T A099505 -19,-224,-104,-373,-99,-408,154,-205,770,222,1655,540,2367,24,2196,
%U A099505 -2196,664,-6440,-1555,-11543,-1750,-14427,4690,-11340,22009,-1595,49534,7008,77051,-5264,85296,-65467,57874
%N A099505 A transform of the Fibonacci numbers.
%C A099505 A transform of A000045 under the mapping g(x) -> (1/(1+x^3)) * g(x/(1+x^3)).
%H A099505 G. C. Greubel, <a href="/A099505/b099505.txt">Table of n, a(n) for n = 0..1000</a>
%H A099505 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-2,1,0,-1).
%F A099505 G.f.: x/(1 - x - x^2 + 2*x^3 - x^4 + x^6).
%F A099505 a(n) = a(n-1) + a(n-2) - 2*a(n-3) + a(n-4) - a(n-6).
%F A099505 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k, k)*(-1)^k*Fibonacci(n-3*k).
%t A099505 LinearRecurrence[{1,1,-2,1,0,-1}, {0,1,1,2,1,2}, 65] (* _G. C. Greubel_, Aug 03 2023 *)
%o A099505 (Magma) I:=[0,1,1,2,1,2]; [n le 6 select I[n] else Self(n-1) +Self(n-2) -2*Self(n-3) +Self(n-4) -Self(n-6): n in [1..65]]; // _G. C. Greubel_, Aug 03 2023
%o A099505 (SageMath)
%o A099505 @CachedFunction
%o A099505 def a(n): # a = A099505
%o A099505 if (n<6): return (0,1,1,2,1,2)[n]
%o A099505 else: return a(n-1) +a(n-2) -2*a(n-3) +a(n-4) -a(n-6)
%o A099505 [a(n) for n in range(71)] # _G. C. Greubel_, Aug 03 2023
%Y A099505 Cf. A000045, A099503, A099504.
%K A099505 easy,sign
%O A099505 0,4
%A A099505 _Paul Barry_, Oct 20 2004