A184635 - OEIS

%I #15 Jun 25 2017 07:30:17

%S 5,16,36,64,100,144,196,256,324,400,484,576,676,784,900,1024,1156,

%T 1296,1444,1600,1764,1936,2116,2304,2500,2704,2916,3136,3364,3600,

%U 3844,4096,4356,4624,4900,5184,5476,5776,6084,6400,6724,7056,7396,7744,8100,8464

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).

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

%F 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 p[n_]:=FractionalPart[(n^4+n)^(1/4)];

%t q[n_]:=Floor[1/p[n]];

%t Table[q[n], {n, 1, 80}]

%t FindLinearRecurrence[Table[q[n], {n, 1, 1000}]]

%t Join[{5},LinearRecurrence[{3,-3,1},{16,36,64},45]] (* _Ray Chandler_, Aug 02 2015 *)

%Y Cf. A184536, A144916, A016742.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 18 2011