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A293400 Greatest integer k such that k/n^2 < (1 + sqrt(5))/2 (the golden ratio).

%I A293400 #12 Sep 08 2022 08:46:19
%S A293400 0,1,6,14,25,40,58,79,103,131,161,195,232,273,317,364,414,467,524,584,
%T A293400 647,713,783,855,931,1011,1093,1179,1268,1360,1456,1554,1656,1762,
%U A293400 1870,1982,2096,2215,2336,2461,2588
%N A293400 Greatest integer k such that k/n^2 < (1 + sqrt(5))/2 (the golden ratio).
%H A293400 Clark Kimberling, <a href="/A293400/b293400.txt">Table of n, a(n) for n = 0..1000</a>
%H A293400 Felipe Gonçalves, Diogo Oliveira e Silva, João P. G. Ramos, <a href="https://arxiv.org/abs/2003.10771">New Sign Uncertainty Principles</a>, arXiv:2003.10771 [math.CA], 2020.
%F A293400 a(n) = floor(r*n^2), where r = (1 + sqrt(5))/2.
%F A293400 a(n) = A293401(n) - 1 for n > 0.
%t A293400 z = 120; r = GoldenRatio;
%t A293400 Table[Floor[r*n^2], {n, 0, z}];   (* A293400 *)
%t A293400 Table[Ceiling[r*n^2], {n, 0, z}]; (* A293401 *)
%t A293400 Table[Round[r*n^2], {n, 0, z}];   (* A293402 *)
%o A293400 (Magma) [Floor((1 + Sqrt(5))/2*n^2) : n in [0..80]]; // _Wesley Ivan Hurt_, Jul 03 2020
%Y A293400 Cf. A001622, A293401, A293402.
%K A293400 nonn,easy
%O A293400 0,3
%A A293400 _Clark Kimberling_, Oct 11 2017