A024116 a(n) = 10^n - n^2.

1, 9, 96, 991, 9984, 99975, 999964, 9999951, 99999936, 999999919, 9999999900, 99999999879, 999999999856, 9999999999831, 99999999999804, 999999999999775, 9999999999999744, 99999999999999711, 999999999999999676

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (13,-33,31,-10).

Crossrefs

Cf. similar sequences listed in A024025.

Programs

Magma

[10^n-n^2: n in [0..20]]; // Vincenzo Librandi, Jun 30 2011

Mathematica

Table[10^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 12 x^2 + 9 x^3)/((1 - 10 x) (1-x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)
LinearRecurrence[{13,-33,31,-10},{1,9,96,991},20] (* Harvey P. Dale, May 29 2021 *)

Formula

G.f.: (1-4*x+12*x^2+9*x^3)/((1-10*x)*(1-x)^3). - Vincenzo Librandi, Oct 06 2014

a(n) = 13*a(n-1) -33*a(n-2) +31*a(n-3) -10*a(n-4) for n>3. - Vincenzo Librandi, Oct 06 2014

a(n) = A011557(n) - A000290(n). - Michel Marcus, Oct 06 2014