A219089 a(n) = floor((n + 1/2)^6).

0, 11, 244, 1838, 8303, 27680, 75418, 177978, 377149, 735091, 1340095, 2313060, 3814697, 6053445, 9294114, 13867245, 20179187, 28722900, 40089475, 54980371, 74220378, 98771297, 129746337, 168425239, 216270112, 274941996

Offset: 0

Author

Clark Kimberling, Jan 01 2013

Keywords

• nonn
• easy

Comments

a(n) is the number k such that {k^p} < 1/2 < {(k+1)^p}, where p = 1/6 and { } = fractional part. Equivalently, the jump sequence of f(x) = x^(1/6), in the sense that these are the nonnegative integers k for which round(k^p) < round((k+1)^p). For details and a guide to related sequences, see A219085.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-22,42,-57,63,-64,64,-64,64,-64,64,-64,64,-64,64,-63,57,-42,22,-7,1).

Crossrefs

Cf. A219085.

Programs

Mathematica

Table[Floor[(n + 1/2)^6], {n, 0, 100}]
LinearRecurrence[{7,-22,42,-57,63,-64,64,-64,64,-64,64,-64,64,-64,64,-63,57,-42,22,-7,1},{0,11,244,1838,8303,27680,75418,177978,377149,735091,1340095,2313060,3814697,6053445,9294114,13867245,20179187,28722900,40089475,54980371,74220378},30] (* Harvey P. Dale, Oct 06 2024 *)

Formula

a(n) = [(n + 1/2)^6].