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A219091 Floor((n + 1/2)^8). 2
0, 25, 1525, 22518, 168151, 837339, 3186448, 10011291, 27249052, 66342043, 147745544, 305902286, 596046447, 1103240376, 1954087550, 3331605615, 5493783665, 8796388244, 13720622866, 20906286173, 31191114176, 45657032334 (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 = 1/8 and { } = fractional part.  Equivalently, the jump sequence of f(x) = x^(1/8), 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 23.  Compare its signature with row 9 of the triangle at A008949.  For which values of p is there a match of this sort between the jump sequence of x^p and row p+1 of the triangle?

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 (9, -37, 93, -163, 219, -247, 255, -256, 256, -256, 256, -256, 256, -256, 256, -255, 247, -219, 163, -93, 37, -9, 1).

FORMULA

a(n) = [(n + 1/2)^8].

MATHEMATICA

Table[Floor[(n + 1/2)^8], {n, 0, 100}]

CROSSREFS

Cf. A219085, A008949.

Sequence in context: A192107 A206465 A138246 * A196299 A196217 A196684

Adjacent sequences:  A219088 A219089 A219090 * A219092 A219093 A219094

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jan 01 2013

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)