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a(n) = 9^n - n^2.
2

%I #15 Sep 08 2022 08:44:48

%S 1,8,77,720,6545,59024,531405,4782920,43046657,387420408,3486784301,

%T 31381059488,282429536337,2541865828160,22876792454765,

%U 205891132094424,1853020188851585,16677181699666280,150094635296998797

%N a(n) = 9^n - n^2.

%H Vincenzo Librandi, <a href="/A024103/b024103.txt">Table of n, a(n) for n = 0..400</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-30,28,-9).

%F G.f.: (1-4*x+11*x^2+8*x^3)/((1-9*x)*(1-x)^3). - _Vincenzo Librandi_, Oct 06 2014

%F a(n) = 12*a(n-1) -30*a(n-2) +28*a(n-3) -9*a(n-4) for n>3. - _Vincenzo Librandi_, Oct 06 2014

%F a(n) = A001019(n) - A000290(n). - _Michel Marcus_, Oct 06 2014

%t Table[9^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 11 x^2 + 8 x^3)/((1 - 9 x) (1 - x)^3), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 06 2014 *)

%o (Magma) [9^n-n^2: n in [0..25]]; // _Vincenzo Librandi_, Jul 06 2011

%Y Cf. A000290, A001019.

%Y Cf. similar sequences listed in A024025.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_