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 A010017 #50 May 07 2024 05:21:48
%S A010017 1,29,110,245,434,677,974,1325,1730,2189,2702,3269,3890,4565,5294,
%T A010017 6077,6914,7805,8750,9749,10802,11909,13070,14285,15554,16877,18254,
%U A010017 19685,21170,22709,24302,25949,27650,29405,31214,33077,34994,36965,38990,41069,43202
%N A010017 a(0) = 1, a(n) = 27*n^2 + 2 for n>0.
%C A010017 From _Bruno Berselli_, Feb 06 2012: (Start)
%C A010017 First trisection of A005918.
%C A010017 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=5, s=1.
%C A010017 After 1, all terms are in A000408. (End)
%H A010017 Bruno Berselli, <a href="/A010017/b010017.txt">Table of n, a(n) for n = 0..1000</a>
%H A010017 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A010017 G.f.: (1+x)*(1+25*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F A010017 E.g.f.: (x*(x+1)*27+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012
%F A010017 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3), n>=4, a(1)=29, a(2)=110, a(3)=245. - _G. C. Greubel_, Aug 02 2015
%F A010017 Sum_{n>=0} 1/a(n) = 3/4+sqrt(6)/36*Pi*coth(Pi*sqrt(6)/9) = 1.0581468172342... - _R. J. Mathar_, May 07 2024
%t A010017 Join[{1}, 27 Range[40]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t A010017 RecurrenceTable[{a[1]==29, a[2]==110, a[3]==245, a[n]== 3*a[n-1] - 3*a[n-2] + a[n-3]}, a, {n, 1,30}] (* _G. C. Greubel_, Aug 02 2015 *)
%o A010017 (PARI) first(m)=my(v=vector(m));for(i=1,m,v[i]=27*(i)^2+2);concat([1],v); /* _Anders Hellström_, Aug 02 2015 */
%o A010017 (Magma) [1] cat [27*n^2+2: n in [1..50]]; // _Vincenzo Librandi_, Aug 03 2015
%Y A010017 Cf. A206399.
%K A010017 nonn,easy
%O A010017 0,2
%A A010017 _N. J. A. Sloane_