%I #34 May 07 2024 05:58:56
%S 1,23,86,191,338,527,758,1031,1346,1703,2102,2543,3026,3551,4118,4727,
%T 5378,6071,6806,7583,8402,9263,10166,11111,12098,13127,14198,15311,
%U 16466,17663,18902,20183,21506,22871,24278,25727,27218,28751,30326,31943,33602,35303
%N a(0) = 1, a(n) = 21*n^2 + 2 for n>0.
%H Bruno Berselli, <a href="/A010011/b010011.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 O.g.f.: 1-x*(23+17*x+2*x^2)/(-1+x)^3. - _R. J. Mathar_, Apr 12 2008
%F E.g.f.: (21*x*(x+1)+2)*e^x-1. - _Gopinath A. R._, Feb 13 2012
%F Sum_{n>=0} 1/a(n) = 3/4+sqrt(42)/84*Pi*coth( Pi*sqrt(42)/21) = 1.0738233857899... - _R. J. Mathar_, May 07 2024
%F a(n) = A069178(n)+A069178(n+1). - _R. J. Mathar_, May 07 2024
%p A010011:=n->`if`(n=0,1,21*n^2+2); seq(A010011(n), n=0..100); # _Wesley Ivan Hurt_, Nov 15 2013
%t Join[{1}, 21 Range[41]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%t Join[{1}, LinearRecurrence[{3, -3, 1}, {23, 86, 191}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o (Magma) [1] cat [21*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_.