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%I #36 May 07 2024 05:56:56
%S 1,22,82,182,322,502,722,982,1282,1622,2002,2422,2882,3382,3922,4502,
%T 5122,5782,6482,7222,8002,8822,9682,10582,11522,12502,13522,14582,
%U 15682,16822,18002,19222,20482,21782,23122,24502,25922,27382,28882,30422,32002,33622
%N a(0) = 1, a(n) = 20*n^2 + 2 for n>0.
%H Bruno Berselli, <a href="/A010010/b010010.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 a(n) = A033571(n)+A158186(n) = A158187(n)*2 for n>0. - _Reinhard Zumkeller_, Mar 13 2009
%F G.f.: (1+x)*(1+18*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F E.g.f.: (x*(x+1)*20+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012
%F Sum_{n>=0} 1/a(n) = 3/4+sqrt(10)/40*Pi*coth(Pi/sqrt(10)) = 1.0772981051444036327... - _R. J. Mathar_, May 07 2024
%F a(n) = A069133(n)+A069133(n+1). - _R. J. Mathar_, May 07 2024
%t Join[{1}, 20 Range[41]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t Join[{1}, LinearRecurrence[{3, -3, 1}, {22, 82, 182}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o (Magma) [1] cat [20*n^2 + 2: n in [1..50]]; // _Vincenzo Librandi_, Aug 03 2015
%Y Cf. A206399.
%K nonn,easy,changed
%O 0,2
%A _N. J. A. Sloane_.
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