A184629 Floor(1/{(5+n^4)^(1/4)}), where {}=fractional part.

1, 7, 22, 51, 100, 173, 274, 409, 583, 800, 1064, 1382, 1757, 2195, 2700, 3276, 3930, 4665, 5487, 6400, 7408, 8518, 9733, 11059, 12500, 14060, 15746, 17561, 19511, 21600, 23832, 26214, 28749, 31443, 34300, 37324, 40522, 43897, 47455, 51200, 55136, 59270, 63605, 68147, 72900, 77868, 83058, 88473, 94119, 100000

Offset

1,2

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1, 0, 1, -3, 3, -1).

Formula

a(n)=floor(1/{(5+n^4)^(1/4)}), where {}=fractional part.

It appears that a(n)=3a(n-1)-3a(n-2)+a(n-3)+a(n-5)-3a(n-6)+3a(n-7)-a(n-8) for n>=15.

Mathematica

p[n_]:=FractionalPart[(n^4+5)^(1/4)]; q[n_]:=Floor[1/p[n]];
  Table[q[n], {n, 1, 80}]
  FindLinearRecurrence[Table[q[n], {n, 1, 1000}]]
Join[{1, 7, 22, 51, 100, 173}, LinearRecurrence[{3, -3, 1, 0, 1, -3, 3, -1}, {274, 409, 583, 800, 1064, 1382, 1757, 2195}, 44]] (* Ray Chandler, Aug 01 2015 *)

Crossrefs

Cf. A184536.

Sequence in context: A211792 A211635 A211634 * A041215 A060822 A011926

Adjacent sequences: A184626 A184627 A184628 * A184630 A184631 A184632

Keyword

nonn

Author

Clark Kimberling, Jan 18 2011

Status

approved