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%I #34 Sep 08 2022 08:45:57
%S 1,9,19,31,45,61,79,99,121,145,171,199,229,261,295,331,369,409,451,
%T 495,541,589,639,691,745,801,859,919,981,1045,1111,1179,1249,1321,
%U 1395,1471,1549,1629,1711,1795,1881,1969,2059,2151,2245,2341
%N a(n) = n^2 + 5*n - 5.
%C Also a(n) = n^2 + 9*n + 9 if the offset is changed to -1. - _R. J. Mathar_, May 18 2011
%H Vincenzo Librandi, <a href="/A190576/b190576.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: x*(-1 - 6*x + 5*x^2) / (x-1)^3. - _R. J. Mathar_, May 18 2011
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=9, a(3)=19. - _Harvey P. Dale_, May 28 2015
%F Sum_{n>=1} 1/a(n) = 199/495 + Pi*tan(3*sqrt(5)*Pi/2)/(3*sqrt(5)). - _Amiram Eldar_, Jan 18 2021
%t k = 5; Table[n^2 + k*n - k, {n, 100}]
%t LinearRecurrence[{3,-3,1},{1,9,19},50] (* _Harvey P. Dale_, May 28 2015 *)
%o (Magma) [n^2+5*n-5: n in [1..50]]; // _Vincenzo Librandi_, Sep 30 2011
%o (PARI) a(n)=n^2+5*n-5 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. sequences of the form n^2 + k*n - k : A000290 (k=0), A028387 (k=1), A028872 (k=2), A082111 (k=3), A028884 (k=4).
%K nonn,easy
%O 1,2
%A _Vladimir Joseph Stephan Orlovsky_, May 12 2011
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