cp's OEIS Frontend

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.

A184635 a(n) = floor(1/{(n+n^4)^(1/4)}), where {} = fractional part.

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%I A184635 #15 Jun 25 2017 07:30:17
%S A184635 5,16,36,64,100,144,196,256,324,400,484,576,676,784,900,1024,1156,
%T A184635 1296,1444,1600,1764,1936,2116,2304,2500,2704,2916,3136,3364,3600,
%U A184635 3844,4096,4356,4624,4900,5184,5476,5776,6084,6400,6724,7056,7396,7744,8100,8464
%N A184635 a(n) = floor(1/{(n+n^4)^(1/4)}), where {} = fractional part.
%H A184635 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F A184635 a(n) = floor(1/{(n+n^4)^(1/4)}), where {} = fractional part.
%F A184635 It appears that a(n)=3a(n-1)-3a(n-2)+a(n-3) for n>=5, and that a(n)=4*n^2 for n>=2.
%t A184635 p[n_]:=FractionalPart[(n^4+n)^(1/4)];
%t A184635 q[n_]:=Floor[1/p[n]];
%t A184635 Table[q[n], {n, 1, 80}]
%t A184635 FindLinearRecurrence[Table[q[n], {n, 1, 1000}]]
%t A184635 Join[{5},LinearRecurrence[{3,-3,1},{16,36,64},45]] (* _Ray Chandler_, Aug 02 2015 *)
%Y A184635 Cf. A184536, A144916, A016742.
%K A184635 nonn
%O A184635 1,1
%A A184635 _Clark Kimberling_, Jan 18 2011