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 A060300 #66 Aug 20 2025 00:27:27
%S A060300 0,16,144,576,1600,3600,7056,12544,20736,32400,48400,69696,97344,
%T A060300 132496,176400,230400,295936,374544,467856,577600,705600,853776,
%U A060300 1024144,1218816,1440000,1690000,1971216,2286144,2637376,3027600,3459600,3936256,4460544,5035536,5664400
%N A060300 a(n) = (2*n*(n+1))^2.
%C A060300 Arises from middle column 4^2, 12^2, 24^2, ... of following triangle: :
%C A060300 3^2 + 4^2 = 5^2
%C A060300 10^2 + 11^2 + 12^2 = 13^2 + 14^2
%C A060300 21^2 + 22^2 + 23^2 + 24^2 = 25^2 + 26^2 + 27^2
%C A060300 36^2 + 37^2 + 38^2 + 39^2 + 40^2 = 41^2 + 42^2 + 43^2 + 44^2
%C A060300 ...
%D A060300 C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, NY, 1966, pp. 90-92.
%H A060300 Harry J. Smith, <a href="/A060300/b060300.txt">Table of n, a(n) for n = 0..1000</a>
%H A060300 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A060300 G.f.: 16*x*(1+4*x+x^2)/(1-x)^5. - _Colin Barker_, Apr 22 2012
%F A060300 a(n) = 4*A035287(n+1) = 4*A002378(n)^2. - _Michel Marcus_, May 24 2016
%F A060300 a(n) = 16*A000537(n) = 16*(n*(n+1)/2)^2 = 16*A000217(n)^2 = A046092(n)^2. - _Bruce J. Nicholson_, Jun 05 2017
%F A060300 a(n) = Integral_{x=1..2*n+1} (x^3-x) dx. - _César Aguilera_, Jun 27 2020
%F A060300 From _Elmo R. Oliveira_, Aug 14 2025: (Start)
%F A060300 E.g.f.: 4*x*(2 + x)*(2 + 6*x + x^2)*exp(x).
%F A060300 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A060300 a(n) = 2*A254371(n) = 8*A163102(n). (End)
%t A060300 CoefficientList[Series[16 x (1 + 4 x + x^2) / (1 - x)^5, {x, 0, 33}], x] (* _Vincenzo Librandi_, Nov 18 2016 *)
%t A060300 Table[(2n(n+1))^2,{n,0,30}] (* _Harvey P. Dale_, Jan 19 2019 *)
%o A060300 (PARI) a(n) = { (2*n*(n + 1))^2 } \\ _Harry J. Smith_, Jul 03 2009
%o A060300 (Magma) [(2*n*(n+1))^2: n in [0..30]]; // _Vincenzo Librandi_, Nov 18 2016
%Y A060300 Cf. A000217, A000537, A002378, A035287, A046092, A163102, A254371.
%K A060300 nonn,easy,changed
%O A060300 0,2
%A A060300 _Jason Earls_, Mar 25 2001
%E A060300 Name corrected by _Harry J. Smith_, Jul 03 2009