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 A010012 #39 Jul 08 2025 01:27:31
%S A010012 1,24,90,200,354,552,794,1080,1410,1784,2202,2664,3170,3720,4314,4952,
%T A010012 5634,6360,7130,7944,8802,9704,10650,11640,12674,13752,14874,16040,
%U A010012 17250,18504,19802,21144,22530,23960,25434,26952,28514,30120,31770,33464,35202,36984
%N A010012 a(0) = 1, a(n) = 22*n^2 + 2 for n>0.
%C A010012 From _Bruno Berselli_, Feb 06 2012: (Start)
%C A010012 First trisection of A008259.
%C A010012 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=2, s=3. After 1, all terms are in A000408. (End)
%H A010012 Bruno Berselli, <a href="/A010012/b010012.txt">Table of n, a(n) for n = 0..1000</a>
%H A010012 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A010012 G.f.: (1+x)*(1+20*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F A010012 E.g.f.: (x*(x+1)*22+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012
%F A010012 Sum_{n>=0} 1/a(n) = 3/4 + sqrt(11)/44*Pi*coth( Pi/sqrt(11)) = 1.0706480516966... - _R. J. Mathar_, May 07 2024
%F A010012 a(n) = A069173(n)+A069173(n+1). - _R. J. Mathar_, May 07 2024
%t A010012 Join[{1}, 22 Range[41]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t A010012 Join[{1},LinearRecurrence[{3,-3,1},{24,90,200},50]] (* _Harvey P. Dale_, Jul 20 2013 *)
%t A010012 CoefficientList[Series[(1 + x) (1 + 20 x + x^2)/(1 - x)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o A010012 (Magma) [1] cat [22*n^2+2: n in [1..50]]; // _Vincenzo Librandi_, Aug 03 2015
%Y A010012 Cf. A206399.
%K A010012 nonn,easy
%O A010012 0,2
%A A010012 _N. J. A. Sloane_