This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A219088 #16 Feb 14 2024 09:11:03
%S A219088 0,7,97,525,1845,5032,11602,23730,44370,77378,127628,201135,305175,
%T A219088 448403,640973,894660,1222981,1641308,2166998,2819506,3620506,4594013,
%U A219088 5766503,7167031,8827351,10782039,13068609,15727636,18802876
%N A219088 a(n) = floor((n + 1/2)^5).
%C A219088 a(n) is the number k such that {k^p} < 1/2 < {(k+1)^p}, where p = 1/5 and { } = fractional part. Equivalently, the jump sequence of f(x) = x^(1/5), in the sense that these are the nonnegative integers k for which round(k^p) < round((k+1)^p). For details and a guide to related sequences, see A219085.
%H A219088 Clark Kimberling, <a href="/A219088/b219088.txt">Table of n, a(n) for n = 0..10000</a>
%H A219088 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1,0,0,0,0,0,0,0,0,0,0,1,-5,10,-10,5,-1).
%F A219088 a(n) = [(n + 1/2)^5].
%F A219088 G.f.: x*(x^19 +3*x^18 +68*x^17 +106*x^16 +121*x^15 +122*x^14 +120*x^13 +118*x^12 +120*x^11 +123*x^10 +116*x^9 +123*x^8 +120*x^7 +118*x^6 +120*x^5 +122*x^4 +120*x^3 +110*x^2 +62*x +7) / ((x -1)^6*(x +1)*(x^2 +1)*(x^4 +1)*(x^8 +1)). - _Colin Barker_, Jan 06 2013
%t A219088 Table[Floor[(n + 1/2)^5], {n, 0, 100}]
%Y A219088 Cf. A219085.
%K A219088 nonn,easy
%O A219088 0,2
%A A219088 _Clark Kimberling_, Jan 01 2013