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 A010003 #37 Jul 08 2025 01:26:44
%S A010003 1,13,46,101,178,277,398,541,706,893,1102,1333,1586,1861,2158,2477,
%T A010003 2818,3181,3566,3973,4402,4853,5326,5821,6338,6877,7438,8021,8626,
%U A010003 9253,9902,10573,11266,11981,12718,13477,14258,15061,15886,16733,17602,18493,19406
%N A010003 a(0) = 1, a(n) = 11*n^2 + 2 for n>0.
%C A010003 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=3, s=1. After 13, all terms are in A000408. - _Bruno Berselli_, Feb 06 2012
%H A010003 Bruno Berselli, <a href="/A010003/b010003.txt">Table of n, a(n) for n = 0..1000</a>
%H A010003 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A010003 G.f.: (1+x)*(1+9*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F A010003 E.g.f.: (x*(x+1)*11+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012
%F A010003 Sum_{n>=0} 1/a(n) = 3/4+sqrt(22)/44*Pi*coth( Pi*sqrt(22)/11) = 1.134242719070... - _R. J. Mathar_, May 07 2024
%t A010003 Join[{1}, 11 Range[41]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t A010003 Join[{1}, LinearRecurrence[{3, -3, 1}, {13, 46, 101}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o A010003 (PARI) A010003(n)=11*n^2+2-!n \\ _M. F. Hasler_, Feb 14 2012
%o A010003 (Magma) [1] cat [11*n^2+2: n in [1..50]]; // _Vincenzo Librandi_, Aug 03 2015
%Y A010003 Cf. A206399.
%K A010003 nonn,easy
%O A010003 0,2
%A A010003 _N. J. A. Sloane_
%E A010003 More terms from _Bruno Berselli_, Feb 06 2012