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A219089 Floor((n + 1/2)^6). 2
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 (list; graph; refs; listen; history; text; internal format)
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}]

CROSSREFS

Cf. A219085.

Sequence in context: A041223 A041220 A347483 * A243683 A323255 A167868

Adjacent sequences:  A219086 A219087 A219088 * A219090 A219091 A219092

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jan 01 2013

STATUS

approved

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Last modified October 6 16:34 EDT 2022. Contains 357270 sequences. (Running on oeis4.)