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%I #18 Sep 08 2022 08:45:54
%S 72,8712,887112,88871112,8888711112,888887111112,88888871111112,
%T 8888888711111112,888888887111111112,88888888871111111112,
%U 8888888888711111111112,888888888887111111111112
%N a(n) = 72 * ((10^n - 1)/9)^2.
%D Walther Lietzmann, Lustiges und Merkwuerdiges von Zahlen und Formen, (F. Hirt, Breslau 1921-43), p. 149.
%H Vincenzo Librandi, <a href="/A178635/b178635.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) = 72*A002477(n) = A002283(n)*A002282(n).
%F a(n) = ((A002282(n-1)*10+7)*10^(n-1)+A002275(n-1))*10+2.
%F G.f.: 72*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - _Ilya Gutkovskiy_, Feb 24 2017
%e n=1: ..................... 72 = 9 * 8;
%e n=2: ................... 8712 = 99 * 88;
%e n=3: ................. 887112 = 999 * 888;
%e n=4: ............... 88871112 = 9999 * 8888;
%e n=5: ............. 8888711112 = 99999 * 88888;
%e n=6: ........... 888887111112 = 999999 * 888888;
%e n=7: ......... 88888871111112 = 9999999 * 8888888;
%e n=8: ....... 8888888711111112 = 99999999 * 88888888;
%e n=9: ..... 888888887111111112 = 999999999 * 888888888.
%t 72 (FromDigits/@Table[PadRight[{}, n, 1], {n, 40}])^2 (* _Vincenzo Librandi_, Mar 21 2014 *)
%o (Magma) [72*((10^n-1)/9)^2: n in [1..50]]; // _Vincenzo Librandi_, Dec 28 2010
%o (PARI) a(n)=72*(10^n\9)^2 \\ _Charles R Greathouse IV_, Jul 02 2013
%Y Cf. A075412, A178630, A178631, A075415, A178632, A178633, A178634, A059988.
%K nonn,easy
%O 1,1
%A _Reinhard Zumkeller_, May 31 2010
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