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 A152728 #36 Mar 04 2023 08:59:24
%S A152728 0,0,0,1,7,19,38,68,110,165,237,327,436,568,724,905,1115,1355,1626,
%T A152728 1932,2274,2653,3073,3535,4040,4592,5192,5841,6543,7299,8110,8980,
%U A152728 9910,10901,11957,13079,14268,15528,16860,18265,19747,21307,22946,24668,26474
%N A152728 a(n) + a(n+1) + a(n+2) = n^3.
%C A152728 The differences between the terms are (1) a(3*k) - a(3*k-1) = 9*k*(k-1)+1; (2) otherwise, a(n) - a(n-1) = (n-2)*(n-1). - _J. M. Bergot_, Jul 10 2013
%C A152728 Second differences give A047266. - _J. M. Bergot_, Dec 01 2014
%H A152728 G. C. Greubel, <a href="/A152728/b152728.txt">Table of n, a(n) for n = 0..5000</a>
%H A152728 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-1).
%F A152728 From _R. J. Mathar_, Aug 15 2010: (Start)
%F A152728 a(n) = ( (n-1)*(n^2-2*n-1) - A057078(n))/3.
%F A152728 G.f.: x^3*(1+4*x+x^2) / ( (1+x+x^2)*(x-1)^4 ). (End)
%F A152728 a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-5). - _Charles R Greathouse IV_, Jul 10 2013
%F A152728 a(3n) = n*(9n^2-9n+1), a(3n+1) = n*(9n^2-2), a(3n+2) = n*(9n^2+9n+1). - _Ralf Stephan_, Jul 12 2013
%F A152728 a(n) = ceiling((n^3 - 3*n^2 + n)/3). - _Robert Israel_, Dec 01 2014
%F A152728 E.g.f.: (3*exp(x)*(1 - x + x^3) - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)))/9. - _Stefano Spezia_, Mar 04 2023
%p A152728 seq(ceil((n^3 - 3*n^2 + n)/3), n=0..100); # _Robert Israel_, Dec 01 2014
%t A152728 k0=k1=0;lst={k0,k1};Do[kt=k1;k1=n^3-k1-k0;k0=kt;AppendTo[lst,k1],{n,1,4!}];lst
%t A152728 LinearRecurrence[{3,-3,2,-3,3,-1}, {0,0,0,1,7,19}, 50] (* _G. C. Greubel_, Sep 01 2018 *)
%o A152728 (PARI) x='x+O('x^50); concat([0,0,0], Vec(x^3*(1+4*x+x^2)/((1+x+x^2)*(x -1)^4 ))) \\ _G. C. Greubel_, Sep 01 2018
%o A152728 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0,0,0] cat Coefficients(R!(x^3*(1+4*x+x^2)/((1+x+x^2)*(x-1)^4))); // _G. C. Greubel_, Sep 01 2018
%Y A152728 Cf. A000578, A047266, A057078.
%K A152728 nonn,easy
%O A152728 0,5
%A A152728 _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008