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A010007 a(0) = 1, a(n) = 17*n^2 + 2 for n>0.

%I A010007 #40 Jul 08 2025 01:27:02
%S A010007 1,19,70,155,274,427,614,835,1090,1379,1702,2059,2450,2875,3334,3827,
%T A010007 4354,4915,5510,6139,6802,7499,8230,8995,9794,10627,11494,12395,13330,
%U A010007 14299,15302,16339,17410,18515,19654,20827,22034,23275,24550,25859,27202,28579
%N A010007 a(0) = 1, a(n) = 17*n^2 + 2 for n>0.
%C A010007 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=2. After 1, all terms are in A000408. - _Bruno Berselli_, Feb 06 2012
%H A010007 Bruno Berselli, <a href="/A010007/b010007.txt">Table of n, a(n) for n = 0..1000</a>
%H A010007 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A010007 G.f.: (1+x)*(1+15*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F A010007 E.g.f. : (x*(x+1)*17+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012
%F A010007 Sum_{n>=0} 1/a(n) = 3/4+sqrt(34)/68*Pi*coth(Pi*sqrt(34)/17) = 1.09001290652... - _R. J. Mathar_, May 07 2024
%F A010007 a(n) = A069130(n)+A069130(n+1). - _R. J. Mathar_, May 07 2024
%t A010007 Join[{1}, 17 Range[41]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t A010007 Join[{1}, LinearRecurrence[{3, -3, 1}, {19, 70, 155}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o A010007 (Magma) [1] cat [17*n^2+2: n in [1..50]]; // _Vincenzo Librandi_, Aug 03 2015
%Y A010007 Cf. A206399.
%K A010007 nonn,easy
%O A010007 0,2
%A A010007 _N. J. A. Sloane_
%E A010007 More terms from _Bruno Berselli_, Feb 06 2012