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 A004697 #35 Sep 08 2022 08:44:33
%S A004697 0,0,0,0,0,1,2,3,5,8,13,22,36,58,94,152,246,399,646,1045,1691,2736,
%T A004697 4427,7164,11592,18756,30348,49104,79452,128557,208010,336567,544577,
%U A004697 881144,1425721,2306866,3732588,6039454
%N A004697 a(n) = floor(Fibonacci(n)/4).
%C A004697 Partial sums of A079962. - _Mircea Merca_, Jan 04 2011
%H A004697 Vincenzo Librandi, <a href="/A004697/b004697.txt">Table of n, a(n) for n = 0..1000</a>
%H A004697 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1,1,0,-1).
%F A004697 G.f.: x^5 / ((1-x)*(1-x-x^2)*(1+x^2+x^4)).
%F A004697 From _Mircea Merca_, Jan 04 2011: (Start)
%F A004697 a(n) = floor(Fibonacci(n)/4).
%F A004697 a(n) = ceiling(Fibonacci(n)/4-3/4).
%F A004697 a(n) = round(Fibonacci(n)/4-3/8).
%F A004697 a(n) = Sum_{k=1..n-2} round(Fibonacci(n)/4).
%F A004697 a(n) = a(n-6) + Fibonacci(n-3), n > 5. (End)
%F A004697 a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-7). - _R. J. Mathar_, Jan 08 2011
%F A004697 a(n) = (A000045(n) - A079343(n))/4. - _R. J. Mathar_, Jul 14 2012
%p A004697 A004697 := proc(n) floor(combinat[fibonacci](n)/4) ; end proc:
%t A004697 CoefficientList[Series[x^5/((1-x)*(1-x-x^2)*(1+x^2+x^4)),{x,0,50}],x] (* _Vincenzo Librandi_, Jul 09 2012 *)
%t A004697 Floor[Fibonacci[Range[0,50]]/4] (* or *) LinearRecurrence[ {2,-1,1,-1,1,0,-1},{0,0,0,0,0,1,2},50] (* _Harvey P. Dale_, Dec 05 2012 *)
%o A004697 (Magma) [Floor(Fibonacci(n)/4): n in [0..40]]; // _Vincenzo Librandi_, Jul 09 2012
%o A004697 (PARI) vector(50, n, n--; fibonacci(n)\4) \\ _G. C. Greubel_, Oct 09 2018
%Y A004697 See A000045 for the Fibonacci numbers.
%Y A004697 Cf. A079962.
%K A004697 nonn,easy
%O A004697 0,7
%A A004697 _N. J. A. Sloane_