OFFSET
0,2
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).
FORMULA
a(n) = [(n + 1/2)^6].
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 01 2013
STATUS
approved