A219089 - OEIS

%I #16 Oct 06 2024 13:57:46

%S 0,11,244,1838,8303,27680,75418,177978,377149,735091,1340095,2313060,

%T 3814697,6053445,9294114,13867245,20179187,28722900,40089475,54980371,

%U 74220378,98771297,129746337,168425239,216270112,274941996

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

%C 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.

%H Clark Kimberling, <a href="/A219089/b219089.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (7,-22,42,-57,63,-64,64,-64,64,-64,64,-64,64,-64,64,-63,57,-42,22,-7,1).

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

%t Table[Floor[(n + 1/2)^6], {n, 0, 100}]

%t 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 *)

%Y Cf. A219085.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jan 01 2013