%I #28 May 07 2024 05:30:38
%S 1,15,54,119,210,327,470,639,834,1055,1302,1575,1874,2199,2550,2927,
%T 3330,3759,4214,4695,5202,5735,6294,6879,7490,8127,8790,9479,10194,
%U 10935,11702,12495,13314,14159,15030,15927,16850,17799,18774,19775,20802,21855,22934
%N a(0) = 1, a(n) = 13*n^2 + 2 for n>0.
%H Bruno Berselli, <a href="/A010004/b010004.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+11*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F E.g.f.: (x*(x+1)*13+2)*e^x-1. - _Gopinath A. R._, Feb 12 2012
%F Sum_{n>=0} 1/a(n) = 3/4+sqrt(26)/52*Pi*coth( Pi*sqrt(26)/13) = 1.1153332151579.. - _R. J. Mathar_, May 07 2024
%t Join[{1}, 13 Range[42]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t Join[{1}, LinearRecurrence[{3, -3, 1}, {15, 54, 119}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o (PARI) A010004(n)=13*n^2+2-!n \\ _M. F. Hasler_, Feb 14 2012
%o (Magma) [1] cat [13*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