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 A172128 #17 Feb 07 2025 05:50:32
%S A172128 1,1,1,1,2,2,4,5,8,12,18,26,40,60,90,137,210,320,492,756,1165,1800,
%T A172128 2786,4320,6710,10440,16266,25380,39650,62016,97108,152213,238824,
%U A172128 375060,589521,927368,1459960,2300100,3626213,5720653,9030450,14263680,22542396,35645400
%N A172128 a(n) = floor(phi^n/n), where phi = golden ratio = (1+sqrt(5))/2.
%H A172128 G. C. Greubel, <a href="/A172128/b172128.txt">Table of n, a(n) for n = 1..4500</a>
%F A172128 a(n) = floor((1/n)*(Fibonacci(n)*phi + Fibonacci(n-1))), where phi = (1+sqrt(5))/2.
%t A172128 Table[Floor[((1 + Sqrt[5])/2)^n/n], {n, 1, 50}]
%t A172128 Table[Floor[GoldenRatio^n/n],{n,50}] (* _Harvey P. Dale_, Dec 12 2018 *)
%o A172128 (Magma) [Floor((Lucas(n) + Sqrt(5)*Fibonacci(n))/(2*n)): n in [1..50]]; // _G. C. Greubel_, Apr 17 2022
%o A172128 (SageMath) [floor(golden_ratio^n/n) for n in (1..50)] # _G. C. Greubel_, Apr 17 2022
%Y A172128 Cf. A000045, A001622 (phi), A181885.
%K A172128 nonn
%O A172128 1,5
%A A172128 _Clark Kimberling_, Nov 20 2010