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%I #33 Sep 08 2022 08:44:37
%S 1,19,70,155,274,427,614,835,1090,1379,1702,2059,2450,2875,3334,3827,
%T 4354,4915,5510,6139,6802,7499,8230,8995,9794,10627,11494,12395,13330,
%U 14299,15302,16339,17410,18515,19654,20827,22034,23275,24550,25859,27202,28579
%N a(0) = 1, a(n) = 17*n^2 + 2 for n>0.
%C 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 Bruno Berselli, <a href="/A010007/b010007.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: (1+x)*(1+15*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F E.g.f. : (x*(x+1)*17+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012
%t Join[{1}, 17 Range[41]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t Join[{1}, LinearRecurrence[{3, -3, 1}, {19, 70, 155}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o (Magma) [1] cat [17*n^2+2: n in [1..50]]; // _Vincenzo Librandi_, Aug 03 2015
%Y Cf. A206399.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Bruno Berselli_, Feb 06 2012
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