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 A293544 #26 Feb 08 2025 22:43:02
%S A293544 0,0,0,1,1,2,3,4,7,11,18,30,48,78,126,203,329,532,861,1394,2255,3649,
%T A293544 5904,9552,15456,25008,40464,65473,105937,171410,277347,448756,726103,
%U A293544 1174859,1900962,3075822,4976784,8052606,13029390,21081995,34111385,55193380
%N A293544 a(n) = round(Fibonacci(n)/3).
%C A293544 a(n) is the integer k that minimizes | k/Fibonacci(n) - 1/3 |.
%H A293544 Clark Kimberling, <a href="/A293544/b293544.txt">Table of n, a(n) for n = 0..1000</a>
%H A293544 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, -1, 1, 1).
%F A293544 G.f.: -(x^2/((-1 + x + x^2) (1 + x^4))).
%F A293544 a(n) = a(n-1) + a(n-2) - a(n-4) + a(n-5) + a(n-6) for n >= 7.
%t A293544 Table[Round[Fibonacci[n]/3], {n, 0, 20}] (* _Eric W. Weisstein_, Feb 08 2025 *)
%t A293544 Round[Fibonacci[Range[0, 20]]/3] (* _Eric W. Weisstein_, Feb 08 2025 *)
%t A293544 LinearRecurrence[{1, 1, 0, -1, 1, 1}, {0, 0, 1, 1, 2, 3}, {0, 20}] (* _Eric W. Weisstein_, Feb 08 2025 *)
%t A293544 CoefficientList[Series[-(x^3/((-1 + x + x^2) (1 + x^4))), {x, 0, 20}], x] (* _Eric W. Weisstein_, Feb 08 2025 *)
%t A293544 Table[(Fibonacci[n] + (-1)^n Sin[n Pi/4] (Cos[n Pi/2] + Sqrt[2] Sin[n Pi/2]))/3, {n, 0, 20}] (* _Eric W. Weisstein_, Feb 08 2025 *)
%Y A293544 Cf. A000045 (Fibonacci(n)).
%Y A293544 Cf. A004696 (floor(Fibonacci(n)/3)).
%Y A293544 Cf. A293543 (ceiling(Fibonacci(n)/3)).
%K A293544 nonn,easy
%O A293544 0,6
%A A293544 _Clark Kimberling_, Oct 12 2017