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 A184533 #31 Jun 13 2025 10:58:22
%S A184533 2,6,13,24,37,54,73,96,121,150,181,216,253,294,337,384,433,486,541,
%T A184533 600,661,726,793,864,937,1014,1093,1176,1261,1350,1441,1536,1633,1734,
%U A184533 1837,1944,2053,2166,2281,2400,2521,2646,2773,2904,3037,3174,3313,3456,3601
%N A184533 a(n) = floor(1/{(2+n^3)^(1/3)}), where {}=fractional part.
%C A184533 Column 2 of the array at A184532.
%H A184533 G. C. Greubel, <a href="/A184533/b184533.txt">Table of n, a(n) for n = 1..5000</a>
%H A184533 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A184533 a(n) = floor(1/{(2+n^3)^(1/3)}), where {}=fractional part.
%F A184533 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F A184533 a(n) = (6*n^2 - (1-(-1)^n))/4 for n>1.
%F A184533 From _Alexander R. Povolotsky_, Aug 22 2011: (Start)
%F A184533 a(n+1) +a(n) = 3*n^2 + 3*n + 1.
%F A184533 G.f.: x*(-2 - 2*x - x^2 - 2*x^3 + x^4)/((-1 + x)^3*(1 + x)). (End)
%F A184533 a(n) = floor(1/((n^3+2)^(1/3)-n)). - _Charles R Greathouse IV_, Aug 23 2011
%F A184533 E.g.f.: (3*x*(x + 1)*cosh(x) + (3*x^2 + 3*x - 1)*sinh(x) + 2*x)/2. - _Stefano Spezia_, Apr 19 2025
%t A184533 p[n_]:=FractionalPart[(n^3+2)^(1/3)]; q[n_]:=Floor[1/p[n]]; Table[q[n],{n,1,120}]
%t A184533 Join[{2},Table[(6*n^2 - (1-(-1)^n))/4,{n,2,50}]] (* or *) Join[{2}, LinearRecurrence[{2,0,-2,1},{6, 13, 24, 37},50]] (* _G. C. Greubel_, Feb 20 2017 *)
%o A184533 (PARI) a(n)=my(x=sqrtn(n^3+2,3));x-=n;1/x\1 \\ _Charles R Greathouse IV_, Aug 23 2011
%o A184533 (PARI) concat([2], for(n=2,25, print1((6*n^2 - (1-(-1)^n))/4, ", "))) \\ _G. C. Greubel_, Feb 20 2017
%Y A184533 Cf. A183532, A183534. Essenitally the same as A032528.
%K A184533 nonn,easy
%O A184533 1,1
%A A184533 _Clark Kimberling_, Jan 16 2011