A198970 a(n) = 4*10^n - 1.

3, 39, 399, 3999, 39999, 399999, 3999999, 39999999, 399999999, 3999999999, 39999999999, 399999999999, 3999999999999, 39999999999999, 399999999999999, 3999999999999999, 39999999999999999, 399999999999999999, 3999999999999999999, 39999999999999999999, 399999999999999999999

Offset: 0

Author

Vincenzo Librandi, Nov 01 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A097166.

Programs

Magma

[4*10^n-1 : n in [0..20]];

Mathematica

CoefficientList[Series[3*(1 + 2*x)/(1 - 11*x + 10*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 03 2013 *)

Formula

a(n) = 3*A097166(n).

a(n) = 10*a(n-1) + 9, n > 0.

a(n) = 11*a(n-1) - 10*a(n-2), n > 1.

G.f.: 3*(1 + 2*x)/(1 - 11*x + 10*x^2). - Vincenzo Librandi, Jan 03 2013

E.g.f.: exp(x)*(4*exp(9*x) - 1). - Elmo R. Oliveira, Sep 10 2024