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%I #50 Feb 08 2024 07:10:05
%S 0,2,22,222,2222,22222,222222,2222222,22222222,222222222,2222222222,
%T 22222222222,222222222222,2222222222222,22222222222222,
%U 222222222222222,2222222222222222,22222222222222222,222222222222222222,2222222222222222222
%N a(n) = 2*(10^n - 1)/9.
%C a(n) = A178630(n)/A002283(n). - _Reinhard Zumkeller_, May 31 2010
%C 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]
%H Ivan Panchenko, <a href="/A002276/b002276.txt">Table of n, a(n) for n = 0..200</a>
%H Kival Ngaokrajang, <a href="/A002276/a002276.pdf">Illustration for n = 1..4</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F From _Vincenzo Librandi_, Jul 22 2010: (Start)
%F a(n) = a(n-1) + 2*10^(n-1) with a(0) = 0.
%F a(n) = 11*a(n-1) - 10*a(n-2) with a(0) = 0, a(1) = 2. (End)
%F G.f.: 2*x/((1 - x)*(1 - 10*x)). - _Ilya Gutkovskiy_, Feb 24 2017
%F E.g.f.: 2*exp(x)*(exp(9*x) - 1)/9. - _Stefano Spezia_, Sep 13 2023
%t LinearRecurrence[{11, -10}, {0, 2}, 50] (* _Jinyuan Wang_, Feb 27 2020 *)
%o (Maxima) A002276(n):=2*(10^n - 1)/9$
%o makelist(A002276(n),n,0,20); /* _Martin Ettl_, Nov 12 2012 */
%o (PARI) a(n)=10^n\9*2 \\ _M. F. Hasler_, Mar 27 2015
%Y Cf. A002275, A002277, A002278, A002279, A002280, A002281, A002282, A178634.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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