login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A219090 a(n) = 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) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) + a(n-64) - 7*a(n-65) + 21*a(n-66) - 35*a(n-67) + 35*a(n-68) - 21*a(n-69) + 7*a(n-70) - a(n-71). - Wesley Ivan Hurt, Jun 18 2022

MATHEMATICA

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

CROSSREFS

Cf. A219085.

Sequence in context: A296790 A330516 A142744 * A222615 A012219 A349783

Adjacent sequences:  A219087 A219088 A219089 * A219091 A219092 A219093

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jan 01 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 28 02:47 EDT 2022. Contains 357063 sequences. (Running on oeis4.)