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 A010008 #47 Jul 08 2025 01:27:08
%S A010008 1,20,74,164,290,452,650,884,1154,1460,1802,2180,2594,3044,3530,4052,
%T A010008 4610,5204,5834,6500,7202,7940,8714,9524,10370,11252,12170,13124,
%U A010008 14114,15140,16202,17300,18434,19604,20810,22052,23330,24644,25994,27380,28802,30260
%N A010008 a(0) = 1, a(n) = 18*n^2 + 2 for n>0.
%C A010008 The identity (18*n^2+2)^2-(9*n^2+2)*(6*n)^2=4 can be written as a(n+1)^2-A010002(n+1)*A008588(n+1)^2=4. - _Vincenzo Librandi_, Feb 07 2012
%H A010008 Bruno Berselli, <a href="/A010008/b010008.txt">Table of n, a(n) for n = 0..1000</a>
%H A010008 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A010008 G.f.: (1+x)*(1+16*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F A010008 a(n) = (3*n-1)^2+(3*n+1)^2 = (n-1)^2+(n+1)^2+(4*n)^2 for n>0. - _Bruno Berselli_, Feb 06 2012
%F A010008 E.g.f.: (x*(x+1)*18+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012
%F A010008 Sum_{n>=0} 1/a(n) = 3/4+ (1/12)*Pi*coth(Pi/3) = 1.0853330948... - _R. J. Mathar_, May 07 2024
%F A010008 a(n) = 2*A247792(n), n>0. - _R. J. Mathar_, May 07 2024
%F A010008 a(n) = A069131(n)+A069131(n+1). - _R. J. Mathar_, May 07 2024
%t A010008 Join[{1}, 18 Range[41]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t A010008 Join[{1}, LinearRecurrence[{3, -3, 1}, {20, 74, 164}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o A010008 (Magma) [1] cat [18*n^2+2: n in [1..50]]; // _Vincenzo Librandi_, Aug 03 2015
%Y A010008 After 20, all terms are in A000408.
%Y A010008 Cf. A206399.
%K A010008 nonn,easy
%O A010008 0,2
%A A010008 _N. J. A. Sloane_
%E A010008 More terms from _Bruno Berselli_, Feb 06 2012