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 A184537 #41 Jun 13 2025 10:58:13
%S A184537 5,3,16,54,128,250,432,686,1024,1458,2000,2662,3456,4394,5488,6750,
%T A184537 8192,9826,11664,13718,16000,18522,21296,24334,27648,31250,35152,
%U A184537 39366,43904,48778,54000,59582,65536,71874,78608,85750,93312,101306,109744,118638,128000,137842,148176,159014,170368,182250,194672,207646,221184,235298,250000,265302,281216,297754,314928,332750,351232,370386,390224,410758,432000,453962,476656
%N A184537 a(n) = floor(1/{(2+n^4)^(1/4)}), where {} = fractional part.
%C A184537 Similar to A033431: replacing a(0) by 0 and a(1) by 2 gives A033431, see next comment.
%C A184537 From _Bruno Berselli_, Feb 04 2011: (Start)
%C A184537 For n >= 1, the value of (n^4+2)^(1/4) is just slightly above n, so the fractional part is (2+n^4)^(1/4)-n. For n > 1, then, 2*n^3 < 1/((2+n^4)^(1/4)-n) < 2*n^3+1.
%C A184537 The proof that 2*n^3*((2+n^4)^(1/4)-n) < 1 follows easily by isolating the quartic root and raising to the 4th power; similarly, 1 < (2*n^3+1)*((2+n^4)^(1/4)-n) needs a sign estimation of a 9th-order polynomial.
%C A184537 In conclusion, a(n)=A033431(n) for n > 1, with g.f. (34*x^2-12*x^3+x^4+x^5+5-17*x) / (x-1)^4. (End)
%H A184537 Vincenzo Librandi, <a href="/A184537/b184537.txt">Table of n, a(n) for n = 0..1000</a>
%H A184537 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A184537 a(n) = floor( 1 / frac((2+n^4)^(1/4)) ).
%F A184537 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 5.
%t A184537 f[n_] := Floor[1/FractionalPart[(n^4 + 2)^(1/4)]]; Array[f, 40, 0]
%t A184537 CoefficientList[Series[(34*x^2-12*x^3+x^4+x^5+5-17*x)/(x-1)^4,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 04 2012 *)
%t A184537 LinearRecurrence[{4,-6,4,-1},{5,3,16,54,128,250},70] (* _Harvey P. Dale_, Apr 06 2018 *)
%o A184537 (Magma) I:=[5, 3, 16, 54, 128,250]; [n le 6 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..70]]; // _Vincenzo Librandi_, Jul 04 2012
%Y A184537 Cf. A184536. Essentially the same as A033431.
%K A184537 nonn,easy
%O A184537 0,1
%A A184537 _Clark Kimberling_, Jan 16 2011