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 A374384 #66 Aug 02 2024 12:19:37
%S A374384 1,12,51,134,281,508,835,1278,1857,2588,3491,4582,5881,7404,9171,
%T A374384 11198,13505,16108,19027,22278,25881,29852,34211,38974,44161,49788,
%U A374384 55875,62438,69497,77068,85171,93822,103041,112844,123251,134278,145945,158268,171267,184958,199361
%N A374384 a(n) = floor(Sum_{k=n^3..(n+1)^3} k^(1/3)).
%H A374384 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A374384 a(n) = floor(3*n^3+9*n^2/2+4*n+1).
%F A374384 a(2*n) = 24*n^3 + 18*n^2 + 8*n + 1.
%F A374384 a(2*n-1) = 24*n^3-18*n^2+8*n-2 for n > 0.
%F A374384 a(2*n) = A248575(2*n) + 4*n + 1.
%F A374384 a(2*n-1) = A248575(2*n-1) + 4*n - 2.
%F A374384 From _Stefano Spezia_, Jul 09 2024: (Start)
%F A374384 G.f.: (1 + 9*x + 17*x^2 + 7*x^3 + 2*x^3)/((1 - x)^4*(1 + x)).
%F A374384 E.g.f.: exp(x)*(1 + 11*x + 14*x^2 + 3*x^3). (End)
%t A374384 Table[Floor[Sum[(n^3+k)^(1/3),{k,0,3n^2+3n+1}]],{n,0,40}] (* _Stefano Spezia_, Jul 07 2024 *)
%o A374384 (PARI) a(n) = 3*n^3+9*n^2\2+4*n+1; \\ _Michel Marcus_, Jul 09 2024
%Y A374384 Cf. A000384, A003215, A005804, A014105, A374489.
%K A374384 nonn,easy
%O A374384 0,2
%A A374384 _Amrit Awasthi_, Jul 07 2024