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A178630 a(n) = 18*((10^n - 1)/9)^2.

%I A178630 #24 Aug 01 2025 00:15:01
%S A178630 18,2178,221778,22217778,2222177778,222221777778,22222217777778,
%T A178630 2222222177777778,222222221777777778,22222222217777777778,
%U A178630 2222222222177777777778,222222222221777777777778,22222222222217777777777778,2222222222222177777777777778,222222222222221777777777777778
%N A178630 a(n) = 18*((10^n - 1)/9)^2.
%H A178630 G. C. Greubel, <a href="/A178630/b178630.txt">Table of n, a(n) for n = 1..200</a>
%H A178630 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A178630 a(n) = 18*A002477(n) = A002283(n)*A002276(n).
%F A178630 a(n)=((A002276(n-1)*10 + 1)*10^(n-1) + A002281(n-1))*10 + 8.
%F A178630 G.f.: 18*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - _Ilya Gutkovskiy_, Feb 24 2017
%F A178630 From _Elmo R. Oliveira_, Jul 30 2025: (Start)
%F A178630 E.g.f.: 2*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/9.
%F A178630 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 3. (End)
%e A178630 n=1: ..................... 18 = 9 * 2;
%e A178630 n=2: ................... 2178 = 99 * 22;
%e A178630 n=3: ................. 221778 = 999 * 222;
%e A178630 n=4: ............... 22217778 = 9999 * 2222;
%e A178630 n=5: ............. 2222177778 = 99999 * 22222;
%e A178630 n=6: ........... 222221777778 = 999999 * 222222;
%e A178630 n=7: ......... 22222217777778 = 9999999 * 2222222;
%e A178630 n=8: ....... 2222222177777778 = 99999999 * 22222222;
%e A178630 n=9: ..... 222222221777777778 = 999999999 * 222222222.
%t A178630 Table[18*((10^n-1)/9)^2, {n, 1, 20}] (* _G. C. Greubel_, Jan 28 2019 *)
%o A178630 (Magma) [18*((10^n - 1)/9)^2: n in [1..20]]; // _Vincenzo Librandi_, Dec 28 2010
%o A178630 (PARI) a(n)=18*(10^n\9)^2 \\ _Charles R Greathouse IV_, Aug 21 2011
%o A178630 (Sage) [18*((10^n-1)/9)^2 for n in (1..20)] # _G. C. Greubel_, Jan 28 2019
%o A178630 (GAP) List([1..20], n -> 18*((10^n-1)/9)^2); # _G. C. Greubel_, Jan 28 2019
%Y A178630 Cf. A059988, A075412, A075415, A178631, A178632, A178633, A178634, A178635.
%Y A178630 Cf. A002276, A002281, A002283, A002477.
%K A178630 nonn,easy
%O A178630 1,1
%A A178630 _Reinhard Zumkeller_, May 31 2010