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 A067725 #50 Feb 26 2022 04:25:40
%S A067725 0,9,24,45,72,105,144,189,240,297,360,429,504,585,672,765,864,969,
%T A067725 1080,1197,1320,1449,1584,1725,1872,2025,2184,2349,2520,2697,2880,
%U A067725 3069,3264,3465,3672,3885,4104,4329,4560,4797,5040,5289,5544,5805,6072,6345,6624
%N A067725 a(n) = 3*n^2 + 6*n.
%C A067725 Numbers h such that 3*(3 + h) is a perfect square. - _Alexander D. Healy_, Tj Tullo, Avery Pickford, Sep 20 2004
%C A067725 Equivalently, numbers k such that k/3+1 is a square. - _Bruno Berselli_, Apr 10 2018
%H A067725 G. C. Greubel, <a href="/A067725/b067725.txt">Table of n, a(n) for n = 0..5000</a>
%H A067725 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A067725 a(n) = 3*A005563(n). - _Zerinvary Lajos_, Mar 06 2007
%F A067725 a(n) = a(n-1) + 6*n + 3, with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 08 2010
%F A067725 From _Colin Barker_, Apr 11 2012: (Start)
%F A067725 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A067725 G.f.: 3*x*(3-x)/(1-x)^3. (End)
%F A067725 E.g.f.: 3*x*(x + 3)*exp(x). - _G. C. Greubel_, Jul 20 2017
%F A067725 From _Amiram Eldar_, Feb 26 2022: (Start)
%F A067725 Sum_{n>=1} 1/a(n) = 1/4.
%F A067725 Sum_{n>=1} (-1)^(n+1)/a(n) = 1/12. (End)
%p A067725 seq(3*n*(n+2), n=0..50); # _G. C. Greubel_, Sep 01 2019
%t A067725 Select[ Range[10000], IntegerQ[ Sqrt[ 3(3 + # )]] & ]
%t A067725 3*(Range[50]^2 -1) (* _G. C. Greubel_, Sep 01 2019 *)
%o A067725 (PARI) a(n)=3*n*(n+2) \\ _Charles R Greathouse IV_, Dec 07 2011
%o A067725 (Magma) [3*n*(n+2): n in [0..50]]; // _G. C. Greubel_, Sep 01 2019
%o A067725 (Sage) [3*n*(n+2) for n in (0..50)] # _G. C. Greubel_, Sep 01 2019
%o A067725 (GAP) List([0..50], n-> 3*n*(n+2)); # _G. C. Greubel_, Sep 01 2019
%Y A067725 Cf. A005563.
%Y A067725 Cf. numbers k such that k*(k + m) is a perfect square: A028560 (k=9), A067728 (k=8), A067727 (k=7), A067726 (k=6), A067724 (k=5), A028347 (k=4), A054000 (k=2), A005563 (k=1).
%K A067725 nonn,easy
%O A067725 0,2
%A A067725 _Robert G. Wilson v_, Feb 05 2002
%E A067725 Edited by _N. J. A. Sloane_, Sep 14 2008 at the suggestion of _R. J. Mathar_