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a(0) = 1, a(n) = 31*n^2 + 2 for n>0.
2

%I #26 May 07 2024 06:07:27

%S 1,33,126,281,498,777,1118,1521,1986,2513,3102,3753,4466,5241,6078,

%T 6977,7938,8961,10046,11193,12402,13673,15006,16401,17858,19377,20958,

%U 22601,24306,26073,27902,29793,31746,33761,35838,37977,40178,42441,44766,47153,49602

%N a(0) = 1, a(n) = 31*n^2 + 2 for n>0.

%H Bruno Berselli, <a href="/A010020/b010020.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+29*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 07 2012

%F E.g.f.: (x*(x+1)*31+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012

%F Sum_{n>=0} 1/a(n) = 3/4 + sqrt(62)/124 *Pi*coth(Pi*sqrt(62)/31) = 1.05093832062... - _R. J. Mathar_, May 07 2024

%t Join[{1}, 31 Range[40]^2 + 2] (* _Bruno Berselli_, Feb 07 2012 *)

%t Join[{1}, LinearRecurrence[{3, -3, 1}, {33, 126, 281}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)

%o (Magma) [1] cat [31*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_.