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

%I A219090 #16 Feb 14 2024 10:00:04
%S A219090 0,17,610,6433,37366,152243,490222,1334838,3205770,6983372,14071004,
%T A219090 26600198,47683715,81721509,134764658,214942297,332956585,502650756,
%U A219090 741655290,1072117239,1521517764,2123582899,2919292602,3957993128
%N A219090 a(n) = floor((n + 1/2)^7).
%C A219090 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.
%H A219090 Clark Kimberling, <a href="/A219090/b219090.txt">Table of n, a(n) for n = 0..10000</a>
%H A219090 <a href="/index/Rec#order_71">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A219090 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
%t A219090 Table[Floor[(n + 1/2)^7], {n, 0, 100}]
%Y A219090 Cf. A219085.
%K A219090 nonn,easy
%O A219090 0,2
%A A219090 _Clark Kimberling_, Jan 01 2013