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A293403 Greatest integer k such that k/n^2 < (3 + sqrt(5))/2.

%I A293403 #5 Oct 11 2017 21:56:48
%S A293403 0,2,10,23,41,65,94,128,167,212,261,316,376,442,513,589,670,756,848,
%T A293403 945,1047,1154,1267,1384,1507,1636,1769,1908,2052,2201,2356,2515,2680,
%U A293403 2851,3026,3207,3392,3584,3780,3982,4188,4400,4618,4840,5068,5301,5539,5783
%N A293403 Greatest integer k such that k/n^2 < (3 + sqrt(5))/2.
%H A293403 Clark Kimberling, <a href="/A293403/b293403.txt">Table of n, a(n) for n = 0..1000</a>
%F A293403 a(n) = floor(r*n^2), where r = (3 + sqrt(5))/2.
%F A293403 a(n) = A293404(n) - 1 for n > 0.
%t A293403 z = 120; r = 1+GoldenRatio;
%t A293403 Table[Floor[r*n^2], {n, 0, z}];   (* A293403 *)
%t A293403 Table[Ceiling[r*n^2], {n, 0, z}]; (* A293404 *)
%t A293403 Table[Round[r*n^2], {n, 0, z}];   (* A293405 *)
%Y A293403 Cf. A001622, A293401, A293404, A293405.
%K A293403 nonn,easy
%O A293403 0,2
%A A293403 _Clark Kimberling_, Oct 11 2017