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 A293543 #25 Feb 08 2025 16:56:00
%S A293543 0,1,1,1,1,2,3,5,7,12,19,30,48,78,126,204,329,533,862,1394,2255,3649,
%T A293543 5904,9553,15456,25009,40465,65473,105937,171410,277347,448757,726103,
%U A293543 1174860,1900963,3075822,4976784,8052606,13029390,21081996,34111385,55193381
%N A293543 a(n) = ceiling(Fibonacci(n)/3).
%C A293543 a(n) is the least integer k such that k/Fibonacci(n) > 1/3.
%H A293543 Clark Kimberling, <a href="/A293543/b293543.txt">Table of n, a(n) for n = 0..1000</a>
%H A293543 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,0,0,0,1,-1,-1)
%F A293543 G.f.: -((x (-1 + x^2 + x^3 + x^7 + x^8))/((-1 + x) (1 + x) (1 + x^2) (-1 + x + x^2) (1 + x^4))).
%F A293543 a(n) = a(n-1) + a(n-2) + a(n-8) - a(n-9) - a(n-10) for n >= 11.
%t A293543 LinearRecurrence[{1, 1, 0, 0, 0, 0, 0, 1, -1, -1}, {0, 1, 1, 1, 1, 2, 3, 5, 7, 12}, 50] (* _Harvey P. Dale_, Oct 18 2018 *)
%t A293543 Table[Ceiling[Fibonacci[n]/3], {n, 0, 20}] (* _Eric W. Weisstein_, Feb 07 2025 *)
%t A293543 Ceiling[Fibonacci[Range[0, 20]]/3] (* _Eric W. Weisstein_, Feb 07 2025 *)
%t A293543 CoefficientList[Series[-x (-1 + x^2 + x^3 + x^7 + x^8)/((-1 + x) (1 + x) (1 + x^2) (-1 + x + x^2) (1 + x^4)), {x, 0, 20}], x] (* _Eric W. Weisstein_, Feb 07 2025 *)
%t A293543 Table[(9 - 6 Cos[n Pi/2] + 8 Fibonacci[n] - (-1)^n (3 + 4 Sin[n Pi/4] (Cos[n Pi/2] + Sqrt[2] Sin[n Pi/2])))/24, {n, 0, 20}] (* _Eric W. Weisstein_, Feb 07 2025 *)
%Y A293543 Cf. A000045.
%Y A293543 Cf. A004696 (floor(Fibonacci(n)/3)).
%Y A293543 Cf. A293544 (round(Fibonacci(n)/3)).
%K A293543 nonn,easy
%O A293543 0,6
%A A293543 _Clark Kimberling_, Oct 12 2017