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 A010002 #42 Jul 08 2025 01:26:38
%S A010002 1,11,38,83,146,227,326,443,578,731,902,1091,1298,1523,1766,2027,2306,
%T A010002 2603,2918,3251,3602,3971,4358,4763,5186,5627,6086,6563,7058,7571,
%U A010002 8102,8651,9218,9803,10406,11027,11666,12323,12998,13691,14402,15131,15878,16643
%N A010002 a(0) = 1, a(n) = 9*n^2 + 2 for n>0.
%C A010002 Apart from the first term, numbers of the form (r^2+2*s^2)*n^2+2 = (r*n)^2+(s*n-1)^2+(s*n+1)^2: in this case is r=1, s=2. After 1, all terms are in A000408. [_Bruno Berselli_, Feb 06 2012]
%C A010002 The identity (18*n^2+2)^2-(9*n^2+2)*(6*n)^2 = 4 can be written as A010008(n+1)^2-a(n+1)*A008588(n+1)^2 = 4. - _Vincenzo Librandi_, Feb 07 2012
%H A010002 Bruno Berselli, <a href="/A010002/b010002.txt">Table of n, a(n) for n = 0..1000</a>
%H A010002 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A010002 G.f.: (1+x)*(1+7*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F A010002 E.g.f.: (x*(x+1)*9+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012
%F A010002 Sum_{n>=0} 1/a(n) = 3/4+sqrt(2)/12 *Pi*coth(Pi/3*sqrt 2) = 1.1606262038.. - _R. J. Mathar_, May 07 2024
%t A010002 Join[{1}, 9 Range[43]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t A010002 Join[{1}, LinearRecurrence[{3, -3, 1}, {11, 38, 83}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o A010002 (PARI) A010002(n)=9*n^2+2-!n \\ _M. F. Hasler_, Feb 14 2012
%o A010002 (Magma) [1] cat [9*n^2+2: n in [1..50]]; // _Vincenzo Librandi_, Aug 03 2015
%Y A010002 Cf. A206399.
%K A010002 nonn,easy
%O A010002 0,2
%A A010002 _N. J. A. Sloane_
%E A010002 More terms from _Bruno Berselli_, Feb 06 2012