

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



