A002276 a(n) = 2*(10^n - 1)/9.

0, 2, 22, 222, 2222, 22222, 222222, 2222222, 22222222, 222222222, 2222222222, 22222222222, 222222222222, 2222222222222, 22222222222222, 222222222222222, 2222222222222222, 22222222222222222, 222222222222222222, 2222222222222222222, 22222222222222222222, 222222222222222222222

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) is also the total number of holes in a variation of a box fractal as in illustration. - Kival Ngaokrajang, May 23 2014 [As observed by Hans Havermann, this seems to be incorrect: e.g., for n = 2 the illustration shows 28 small holes plus two larger holes. - M. F. Hasler, Oct 05 2020]

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..200
• Kival Ngaokrajang, Illustration for n = 1..4.
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A002275, A002277, A002278, A002279, A002280, A002281, A002282, A002283, A178630, A178634.

Cf. A010785, A017185.

Programs

Mathematica

LinearRecurrence[{11, -10}, {0, 2}, 50] (* Jinyuan Wang, Feb 27 2020 *)

Maxima

A002276(n):=2*(10^n - 1)/9$
makelist(A002276(n),n,0,20); /* Martin Ettl, Nov 12 2012 */

PARI

a(n)=10^n\9*2 \\ M. F. Hasler, Mar 27 2015

Formula

a(n) = A178630(n)/A002283(n). - Reinhard Zumkeller, May 31 2010

From Vincenzo Librandi, Jul 22 2010: (Start)

a(n) = a(n-1) + 2*10^(n-1) with a(0) = 0.

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

G.f.: 2*x/((1 - x)*(1 - 10*x)). - Ilya Gutkovskiy, Feb 24 2017

E.g.f.: 2*exp(x)*(exp(9*x) - 1)/9. - Stefano Spezia, Sep 13 2023

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

a(n) = 2*A002275(n).

a(n) = A010785(A017185(n-1)) for n >= 1. (End)