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 A219091 #20 Feb 14 2024 09:08:31
%S A219091 0,25,1525,22518,168151,837339,3186448,10011291,27249052,66342043,
%T A219091 147745544,305902286,596046447,1103240376,1954087550,3331605615,
%U A219091 5493783665,8796388244,13720622866,20906286173,31191114176,45657032334
%N A219091 a(n) = floor((n + 1/2)^8).
%C A219091 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?
%C A219091 For details and a guide to related sequences, see A219085.
%H A219091 Clark Kimberling, <a href="/A219091/b219091.txt">Table of n, a(n) for n = 0..10000</a>
%H A219091 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (9, -37, 93, -163, 219, -247, 255, -256, 256, -256, 256, -256, 256, -256, 256, -255, 247, -219, 163, -93, 37, -9, 1).
%t A219091 Table[Floor[(n + 1/2)^8], {n, 0, 100}]
%Y A219091 Cf. A219085, A008949.
%K A219091 nonn,easy
%O A219091 0,2
%A A219091 _Clark Kimberling_, Jan 01 2013