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a(0) = 1, a(n) = 15*n^2 + 2 for n>0.
2

%I #28 May 07 2024 05:46:35

%S 1,17,62,137,242,377,542,737,962,1217,1502,1817,2162,2537,2942,3377,

%T 3842,4337,4862,5417,6002,6617,7262,7937,8642,9377,10142,10937,11762,

%U 12617,13502,14417,15362,16337,17342,18377,19442,20537,21662,22817,24002,25217,26462

%N a(0) = 1, a(n) = 15*n^2 + 2 for n>0.

%H Bruno Berselli, <a href="/A010005/b010005.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+13*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012

%F E.g.f.: (x*(x+1)*15+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012

%F Sum_{n>=0} 1/a(n) = 3/4+sqrt(30)/60*Pi*coth(Pi *sqrt(30)/15) = 1.101107302494... - _R. J. Mathar_, May 07 2024

%t Join[{1}, 15 Range[42]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)

%t Join[{1}, LinearRecurrence[{3, -3, 1}, {17, 62, 137}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)

%o (PARI) A010005(n)=15*n^2+2-!n \\ _M. F. Hasler_, Feb 14 2012

%o (Magma) [1] cat [15*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