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 A006137 #46 Feb 19 2024 01:49:00
%S A006137 1,6,20,43,75,116,166,225,293,370,456,551,655,768,890,1021,1161,1310,
%T A006137 1468,1635,1811,1996,2190,2393,2605,2826,3056,3295,3543,3800,4066,
%U A006137 4341,4625,4918,5220,5531,5851,6180,6518,6865,7221,7586,7960,8343,8735,9136,9546
%N A006137 a(n) = 1 + n/2 + 9*n^2/2.
%C A006137 72*a(n) - 71 = (18*n+1)^2 = A161705(n)^2 is a perfect square. - _Klaus Purath_, Jan 14 2022
%H A006137 Harvey P. Dale, <a href="/A006137/b006137.txt">Table of n, a(n) for n = 0..1000</a>
%H A006137 Nickolas Arustamyan, Christopher Cox, Erik Lundberg, Sean Perry, and Zvi Rosen, <a href="https://arxiv.org/abs/2106.11416">On the Number of Equilibria Balancing Newtonian Point Masses with a Central Force</a>, arXiv:2106.11416 [math-ph], 2021.
%H A006137 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A006137 a(n) = a(n-1) + 9*n - 4 (with a(0)=1). - _Vincenzo Librandi_, Nov 18 2010
%F A006137 From _Klaus Purath_, Jan 14 2022: (Start)
%F A006137 a(n) = A276819(n) + n.
%F A006137 A003215(a(n)) - A003215(a(n)-3) = A002378(9*n). (End)
%F A006137 From _Stefano Spezia_, Dec 25 2022: (Start)
%F A006137 O.g.f.: (1 + 3*x+ 5*x^2)/(1 - x)^3.
%F A006137 E.g.f.: exp(x)*(2 + 10*x + 9*x^2)/2. (End)
%t A006137 Table[1+n/2+9 n^2/2,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{1,6,20},40] (* _Harvey P. Dale_, Oct 05 2012 *)
%o A006137 (PARI) a(n)=1+n/2+9*n^2/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A006137 Cf. A002378, A003215, A161705, A276819.
%K A006137 nonn,easy
%O A006137 0,2
%A A006137 _N. J. A. Sloane_