A184631 Floor(1/{(7+n^4)^(1/4)}), where {}=fractional part.

1, 5, 15, 36, 71, 123, 196, 292, 416, 571, 760, 987, 1255, 1568, 1928, 2340, 2807, 3332, 3919, 4571, 5292, 6084, 6952, 7899, 8928, 10043, 11247, 12544, 13936, 15428, 17023, 18724, 20535, 22459, 24500, 26660, 28944, 31355, 33896, 36571, 39383, 42336, 45432, 48676, 52071, 55620, 59327, 63195, 67228, 71428, 75800

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, 0, 0, 1, -3, 3, -1).

Formula

a(n)=floor(1/{(7+n^4)^(1/4)}), where {}=fractional part.

It appears that a(n)=3a(n-1)-3a(n-2)+a(n-3)+a(n-7)-3a(n-8)+3a(n-9)-a(n-10) for n>=13.

Mathematica

p[n_]:=FractionalPart[(n^4+7)^(1/4)]; q[n_]:=Floor[1/p[n]];
  Table[q[n], {n, 1, 80}]
  FindLinearRecurrence[Table[q[n], {n, 1, 1000}]]
Join[{1, 5}, LinearRecurrence[{3, -3, 1, 0, 0, 0, 1, -3, 3, -1}, {15, 36, 71, 123, 196, 292, 416, 571, 760, 987}, 49]] (* Ray Chandler, Aug 02 2015 *)

Crossrefs

Cf. A184536.

Sequence in context: A220480 A105720 A174655 * A366971 A011933 A093802

Adjacent sequences: A184628 A184629 A184630 * A184632 A184633 A184634

Keyword

nonn

Author

Clark Kimberling, Jan 18 2011

Status

approved