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 A054602 #80 Aug 11 2025 18:16:05
%S A054602 0,3,12,33,72,135,228,357,528,747,1020,1353,1752,2223,2772,3405,4128,
%T A054602 4947,5868,6897,8040,9303,10692,12213,13872,15675,17628,19737,22008,
%U A054602 24447,27060,29853,32832,36003,39372,42945,46728,50727,54948,59397,64080,69003,74172
%N A054602 a(n) = Sum_{d|3} phi(d)*n^(3/d).
%C A054602 Every term is the product plus the sum of 3 consecutive numbers. - _Vladimir Joseph Stephan Orlovsky_, Oct 24 2009
%C A054602 Continued fraction [n,n,n] = (n^2+1)/(n^3+2n) = (n^2+1)/a(n); e.g., [7,7,7] = 50/357. - _Gary W. Adamson_, Jul 15 2010
%H A054602 Seiichi Manyama, <a href="/A054602/b054602.txt">Table of n, a(n) for n = 0..10000</a>
%H A054602 Thomas Oléron Evans, <a href="http://www.mathistopheles.co.uk/2015/08/22/queues-of-cubes/">Queues of Cubes</a>, Mathistopheles, August 22 2015.
%H A054602 Aleksandar Petojević, <a href="http://dx.doi.org/10.5937/MatMor0801037P">A Note about the Pochhammer Symbol</a>, Mathematica Moravica, Vol. 12-1 (2008), pp. 37-42.
%H A054602 Michelle Rudolph-Lilith, <a href="http://arxiv.org/abs/1508.07894">On the Product Representation of Number Sequences, with Application to the Fibonacci Family</a>, arXiv preprint arXiv:1508.07894 [math.NT], 2015.
%H A054602 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A054602 a(n) = n^3 + 2*n = A073133(n,3). - _Henry Bottomley_, Jul 16 2002
%F A054602 G.f.: 3*x*(x^2+1)/(x-1)^4. - _Colin Barker_, Dec 21 2012
%F A054602 a(n) = ((n-1)^3 + n^3 + (n+1)^3)/3. - _David Morales Marciel_, Aug 28 2015
%F A054602 From _Bernard Schott_, Nov 28 2021: (Start)
%F A054602 a(n) = A007531(n+1) + A008585(n) (see 1st comment).
%F A054602 a(n) = 3*A006527(n). (End)
%F A054602 From _Elmo R. Oliveira_, Aug 09 2025: (Start)
%F A054602 E.g.f.: exp(x)*x*(3 + 3*x + x^2).
%F A054602 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A054602 a(n) = A292022(n)/4. (End)
%t A054602 nterms=100;Table[n^3+2n,{n,0,nterms}] (* _Paolo Xausa_, Nov 25 2021 *)
%o A054602 (PARI) a(n)=n^3+2*n \\ _Charles R Greathouse IV_, Sep 01 2015
%Y A054602 Row n=3 of A185651.
%Y A054602 Cf. A006527, A007531, A008585, A073133, A292022.
%K A054602 nonn,easy
%O A054602 0,2
%A A054602 _N. J. A. Sloane_, Apr 16 2000