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A219090 Floor((n + 1/2)^7). 2
0, 17, 610, 6433, 37366, 152243, 490222, 1334838, 3205770, 6983372, 14071004, 26600198, 47683715, 81721509, 134764658, 214942297, 332956585, 502650756, 741655290, 1072117239, 1521517764, 2123582899, 2919292602, 3957993128 (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 = 1/7 and { } = fractional part.  Equivalently, the jump sequence of f(x) = x^(1/7), in the sense that these are the nonnegative integers k for which round(k^p) < round((k+1)^p).  It appears that the sequence is linearly recurrent with order 71.  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, -21, 35, -35, 21, -7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -7, 21, -35, 35, -21, 7, -1).

FORMULA

a(n) = [(n + 1/2)^7].

MATHEMATICA

Table[Floor[(n + 1/2)^7], {n, 0, 100}]

CROSSREFS

Cf. A219085.

Sequence in context: A296790 A330516 A142744 * A222615 A012219 A219075

Adjacent sequences:  A219087 A219088 A219089 * A219091 A219092 A219093

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jan 01 2013

STATUS

approved

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Last modified September 27 04:10 EDT 2021. Contains 347673 sequences. (Running on oeis4.)