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

5, 16, 36, 64, 100, 144, 196, 256, 324, 400, 484, 576, 676, 784, 900, 1024, 1156, 1296, 1444, 1600, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 6084, 6400, 6724, 7056, 7396, 7744, 8100, 8464

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Formula

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

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.

Mathematica

p[n_]:=FractionalPart[(n^4+n)^(1/4)];
q[n_]:=Floor[1/p[n]];
Table[q[n], {n, 1, 80}]
FindLinearRecurrence[Table[q[n], {n, 1, 1000}]]
Join[{5}, LinearRecurrence[{3, -3, 1}, {16, 36, 64}, 45]] (* Ray Chandler, Aug 02 2015 *)

Crossrefs

Cf. A184536, A144916, A016742.

Sequence in context: A363605 A108966 A321019 * A328506 A072333 A055232

Adjacent sequences: A184632 A184633 A184634 * A184636 A184637 A184638

Keyword

nonn

Author

Clark Kimberling, Jan 18 2011

Status

approved