A024103 a(n) = 9^n - n^2.

1, 8, 77, 720, 6545, 59024, 531405, 4782920, 43046657, 387420408, 3486784301, 31381059488, 282429536337, 2541865828160, 22876792454765, 205891132094424, 1853020188851585, 16677181699666280, 150094635296998797

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (12,-30,28,-9).

Crossrefs

Cf. A000290, A001019.

Cf. similar sequences listed in A024025.

Programs

Magma

[9^n-n^2: n in [0..25]]; // Vincenzo Librandi, Jul 06 2011

Mathematica

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 *)

Formula

G.f.: (1-4*x+11*x^2+8*x^3)/((1-9*x)*(1-x)^3). - Vincenzo Librandi, Oct 06 2014

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

a(n) = A001019(n) - A000290(n). - Michel Marcus, Oct 06 2014