%I #20 Sep 08 2022 08:45:54
%S 18,2178,221778,22217778,2222177778,222221777778,22222217777778,
%T 2222222177777778,222222221777777778,22222222217777777778,
%U 2222222222177777777778,222222222221777777777778
%N a(n) = 18 * ((10^n - 1)/9)^2.
%H G. C. Greubel, <a href="/A178630/b178630.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F a(n) = 18*A002477(n) = A002283(n)*A002276(n).
%F a(n)=((A002276(n-1)*10 + 1)*10^(n-1) + A002281(n-1))*10 + 8.
%F G.f.: 18*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - _Ilya Gutkovskiy_, Feb 24 2017
%e n=1: ..................... 18 = 9 * 2;
%e n=2: ................... 2178 = 99 * 22;
%e n=3: ................. 221778 = 999 * 222;
%e n=4: ............... 22217778 = 9999 * 2222;
%e n=5: ............. 2222177778 = 99999 * 22222;
%e n=6: ........... 222221777778 = 999999 * 222222;
%e n=7: ......... 22222217777778 = 9999999 * 2222222;
%e n=8: ....... 2222222177777778 = 99999999 * 22222222;
%e n=9: ..... 222222221777777778 = 999999999 * 222222222.
%t Table[18*((10^n-1)/9)^2, {n, 1, 20}] (* _G. C. Greubel_, Jan 28 2019 *)
%o (Magma) [18*((10^n - 1)/9)^2: n in [1..20]]; // _Vincenzo Librandi_, Dec 28 2010
%o (PARI) a(n)=18*(10^n\9)^2 \\ _Charles R Greathouse IV_, Aug 21 2011
%o (Sage) [18*((10^n-1)/9)^2 for n in (1..20)] # _G. C. Greubel_, Jan 28 2019
%o (GAP) List([1..20], n -> 18*((10^n-1)/9)^2); # _G. C. Greubel_, Jan 28 2019
%Y Cf. A075412, A178631, A075415, A178632, A178633, A178634, A178635, A059988.
%K nonn,easy
%O 1,1
%A _Reinhard Zumkeller_, May 31 2010