A002278 a(n) = 4*(10^n - 1)/9.

0, 4, 44, 444, 4444, 44444, 444444, 4444444, 44444444, 444444444, 4444444444, 44444444444, 444444444444, 4444444444444, 44444444444444, 444444444444444, 4444444444444444, 44444444444444444, 444444444444444444, 4444444444444444444, 44444444444444444444, 444444444444444444444

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A002275, A002276, A002277, A002279, A002280, A002281, A002282, A002283, A075415, A178632.

Cf. A007091, A010785, A017209, A024049.

Programs

Mathematica

LinearRecurrence[{11, -10}, {0, 4}, 20] (* Robert G. Wilson v, Jul 06 2013 *)

PARI

a(n)=4*(10^n-1)/9 \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = A075415(n)/A002283(n). - Reinhard Zumkeller, May 31 2010

From Vincenzo Librandi, Jul 22 2010: (Start)

a(n) = a(n-1) + 4*10^(n-1) with a(0)=0;

a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0, a(1)=4. (End)

G.f.: 4*x/((1 - x)*(1 - 10*x)). - Ilya Gutkovskiy, Feb 24 2017

E.g.f.: 4*exp(x)*(exp(9*x) - 1)/9. - Stefano Spezia, Sep 13 2023

a(n) = A007091(A024049(n)). - Michel Marcus, Jun 16 2024

From Elmo R. Oliveira, Jul 19 2025: (Start)

a(n) = 4*A002275(n).

a(n) = A010785(A017209(n-1)) for n >= 1. (End)