A219091 a(n) = floor((n + 1/2)^8).

0, 25, 1525, 22518, 168151, 837339, 3186448, 10011291, 27249052, 66342043, 147745544, 305902286, 596046447, 1103240376, 1954087550, 3331605615, 5493783665, 8796388244, 13720622866, 20906286173, 31191114176, 45657032334

Offset: 0

Author

Clark Kimberling, Jan 01 2013

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A219085, A008949.

Programs

Mathematica

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