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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 01 2013
STATUS
approved