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 A074677 #26 Jan 15 2024 16:26:34
%S A074677 0,1,1,1,2,4,6,9,15,25,40,64,104,169,273,441,714,1156,1870,3025,4895,
%T A074677 7921,12816,20736,33552,54289,87841,142129,229970,372100,602070,
%U A074677 974169,1576239,2550409,4126648,6677056,10803704,17480761,28284465,45765225,74049690
%N A074677 a(n) = Sum_{i = 0..floor(n/2)} (-1)^(i + floor(n/2)) F(2*i + e), where F = A000045 (Fibonacci numbers) and e = (1-(-1)^n)/2.
%C A074677 Essentially the same as A006498 (g.f. 1/(1-x-x^3-x^4)).
%C A074677 a(n) is the convolution of F(n) with the sequence (1,0,-1,0,1,0,-1,0,...), A056594.
%H A074677 Reinhard Zumkeller, <a href="/A074677/b074677.txt">Table of n, a(n) for n = 0..1000</a>
%H A074677 Victoria Zhuravleva, <a href="http://dx.doi.org/10.5802/jtnb.846">Diophantine approximations with Fibonacci numbers</a>, Journal de théorie des nombres de Bordeaux, 25 no. 2 (2013), p. 499-520. See Lemma 5.1.
%H A074677 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1).
%F A074677 a(n) = a(n-1) + a(n-3) + a(n-4) for n>3, a(0)=0, a(1)=1, a(2)=1, a(3)=1.
%F A074677 G.f.: x/(1 - x - x^3 - x^4).
%F A074677 a(n) = Fibonacci(ceiling(n/2))*Fibonacci(floor(n/2+1)). - _Alois P. Heinz_, Jan 15 2024
%t A074677 CoefficientList[Series[x/(1 - x - x^3 - x^4), {x, 0, 40}], x]
%o A074677 (Haskell)
%o A074677 a074677 n = a074677_list !! (n-1)
%o A074677 a074677_list = 0 : 1 : 1 : 1 : zipWith (+) a074677_list
%o A074677 (zipWith (+) (tail a074677_list) (drop 3 a074677_list))
%o A074677 -- _Reinhard Zumkeller_, Dec 28 2011
%o A074677 (Sage) [sum((-1)^(i+floor(n/2))*fibonacci(2*i+(1-(-1)^n)/2) for i in (0..floor(n/2))) for n in [0..50]]; # _Bruno Berselli_, Mar 15 2016
%o A074677 (Magma) [&+[(-1)^(i+Floor(n/2))*Fibonacci(2*i+(1-(-1)^n) div 2): i in [0..Floor(n/2)]]: n in [0..50]]; // _Bruno Berselli_, Mar 15 2016
%o A074677 (PARI) concat(0, Vec(x/((1+x^2)*(1-x-x^2)) + O(x^50))) \\ _Colin Barker_, Mar 15 2016
%Y A074677 Cf. A000045, A056594.
%K A074677 nonn,easy
%O A074677 0,5
%A A074677 Mario Catalani (mario.catalani(AT)unito.it), Aug 30 2002