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 A153644 #39 Mar 02 2023 02:54:30
%S A153644 42,82,130,186,250,322,402,490,586,690,802,922,1050,1186,1330,1482,
%T A153644 1642,1810,1986,2170,2362,2562,2770,2986,3210,3442,3682,3930,4186,
%U A153644 4450,4722,5002,5290,5586,5890,6202,6522,6850,7186,7530,7882,8242,8610,8986,9370
%N A153644 a(n) = 4*n^2 + 28*n + 10.
%C A153644 Sequence gives values of x such that x^3 + 39x^2 = y^2 since a(n)^3 + 39*a(n)^2 = (8n^3 + 84n^2 + 216n + 70)^2.
%C A153644 a(n) = 2*(seventh diagonal to A153238).
%C A153644 About the first comment, naturally, the complete list of nonnegative values of x in x^3 + 39*x^2 = y^2 is given by x = m^2-39 with m>6. - _Bruno Berselli_, Jan 25 2012
%H A153644 Vincenzo Librandi, <a href="/A153644/b153644.txt">Table of n, a(n) for n = 1..10000</a>
%H A153644 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A153644 From _Colin Barker_, Jan 24 2012: (Start)
%F A153644 a(1)=42, a(2)=82, a(3)=130, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A153644 G.f.: 2*x*((3-x)*(7-5*x))/(1-x)^3. (End)
%F A153644 E.g.f.: 2*(-5 + (5 + 16*x + 2*x^2)*exp(x)). - _G. C. Greubel_, Aug 23 2016
%F A153644 Sum_{n>=1} 1/a(n) = 62/1995 + tan(sqrt(39)*Pi/2)*Pi/(4*sqrt(39)). - _Amiram Eldar_, Mar 02 2023
%t A153644 LinearRecurrence[{3,-3,1},{42,82,130}, 25] (* _G. C. Greubel_, Aug 23 2016 *)
%t A153644 Table[4n^2+28n+10,{n,70}] (* _Harvey P. Dale_, Jan 15 2023 *)
%o A153644 (PARI) a(n)=4*n*(n+7)+10 \\ _Charles R Greathouse IV_, Jan 24 2012
%o A153644 (Magma) [4*n^2 + 28*n + 10: n in [1..50]]; // _Vincenzo Librandi_, Jan 25 2012
%Y A153644 Cf. A153238, A067076.
%K A153644 nonn,easy,less
%O A153644 1,1
%A A153644 _Vincenzo Librandi_, Dec 30 2008