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A181718 a(n) = (1/9)*(10^(2*n) + 10^n - 2).

%I A181718 #44 Mar 26 2024 04:09:33
%S A181718 0,12,1122,111222,11112222,1111122222,111111222222,11111112222222,
%T A181718 1111111122222222,111111111222222222,11111111112222222222,
%U A181718 1111111111122222222222,111111111111222222222222,11111111111112222222222222,1111111111111122222222222222
%N A181718 a(n) = (1/9)*(10^(2*n) + 10^n - 2).
%C A181718 In decimal, n times 1 followed by n times 2.
%C A181718 a(n) = 3 + 3*3, 33 + 33*33, 333 + 333*333, written with 3,6,9,12,... = A008585(n+1) 3's.
%H A181718 Vincenzo Librandi, <a href="/A181718/b181718.txt">Table of n, a(n) for n = 0..200</a>
%H A181718 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A181718 a(n) = A002277(n)*A093137(n).
%F A181718 G.f.: 6*x*(2-35*x) / ( (1-x)*(1-10*x)*(1-100*x) ). - _R. J. Mathar_, Feb 28 2011
%F A181718 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3), a(0)=0, a(1)=12, a(2)=1122. - _Harvey P. Dale_, Jul 31 2013
%F A181718 a(n) = (A074992(n) - 1)/3. - _Michel Marcus_, Sep 14 2013
%F A181718 E.g.f.: (1/9)*(-2*exp(x) + exp(10*x) + exp(100*x)). - _G. C. Greubel_, Mar 25 2024
%t A181718 Table[FromDigits[Join[PadRight[{},n,1],PadRight[{},n,2]]],{n,0,20}] (* or *) LinearRecurrence[{111,-1110,1000},{0,12,1122},20] (* _Harvey P. Dale_, Jul 31 2013 *)
%o A181718 (Magma) [(1/9)*(10^(2*n) + 10^n - 2): n in [0..20]]; // _Vincenzo Librandi_, Aug 04 2011
%o A181718 (PARI) vector(30, n, n--; (10^(2*n) + 10^n - 2)/9) \\ _G. C. Greubel_, Nov 02 2018
%o A181718 (Python)
%o A181718 for n in range(30):
%o A181718     print((10**(2*n)+10**n-2)//9, end=', ')
%o A181718 # _Stefano Spezia_, Nov 02 2018
%o A181718 (SageMath) [(100^n +10^n -2)//9 for n in range(31)] # _G. C. Greubel_, Mar 25 2024
%Y A181718 Cf. A002277, A008585, A074992, A093137.
%K A181718 nonn,easy
%O A181718 0,2
%A A181718 _Paul Curtz_, Nov 17 2010