A219090 a(n) = floor((n + 1/2)^7).

0, 17, 610, 6433, 37366, 152243, 490222, 1334838, 3205770, 6983372, 14071004, 26600198, 47683715, 81721509, 134764658, 214942297, 332956585, 502650756, 741655290, 1072117239, 1521517764, 2123582899, 2919292602, 3957993128

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 = 1/7 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).

Crossrefs

Cf. A219085.

Programs

Mathematica

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

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