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A178635 a(n) = 72*((10^n - 1)/9)^2.

%I A178635 #23 Aug 01 2025 11:09:14
%S A178635 72,8712,887112,88871112,8888711112,888887111112,88888871111112,
%T A178635 8888888711111112,888888887111111112,88888888871111111112,
%U A178635 8888888888711111111112,888888888887111111111112,88888888888871111111111112,8888888888888711111111111112,888888888888887111111111111112
%N A178635 a(n) = 72*((10^n - 1)/9)^2.
%D A178635 Walther Lietzmann, Lustiges und Merkwuerdiges von Zahlen und Formen, (F. Hirt, Breslau 1921-43), p. 149.
%H A178635 Vincenzo Librandi, <a href="/A178635/b178635.txt">Table of n, a(n) for n = 1..200</a>
%H A178635 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A178635 a(n) = 72*A002477(n) = A002283(n)*A002282(n).
%F A178635 a(n) = ((A002282(n-1)*10 + 7)*10^(n-1) + A002275(n-1))*10 + 2.
%F A178635 G.f.: 72*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - _Ilya Gutkovskiy_, Feb 24 2017
%F A178635 From _Elmo R. Oliveira_, Aug 01 2025: (Start)
%F A178635 E.g.f.: 8*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/9.
%F A178635 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 3. (End)
%e A178635 n=1: ..................... 72 = 9 * 8;
%e A178635 n=2: ................... 8712 = 99 * 88;
%e A178635 n=3: ................. 887112 = 999 * 888;
%e A178635 n=4: ............... 88871112 = 9999 * 8888;
%e A178635 n=5: ............. 8888711112 = 99999 * 88888;
%e A178635 n=6: ........... 888887111112 = 999999 * 888888;
%e A178635 n=7: ......... 88888871111112 = 9999999 * 8888888;
%e A178635 n=8: ....... 8888888711111112 = 99999999 * 88888888;
%e A178635 n=9: ..... 888888887111111112 = 999999999 * 888888888.
%t A178635 72 (FromDigits/@Table[PadRight[{}, n, 1], {n, 40}])^2 (* _Vincenzo Librandi_, Mar 21 2014 *)
%o A178635 (Magma) [72*((10^n-1)/9)^2: n in [1..50]]; // _Vincenzo Librandi_, Dec 28 2010
%o A178635 (PARI) a(n)=72*(10^n\9)^2 \\ _Charles R Greathouse IV_, Jul 02 2013
%Y A178635 Cf. A059988, A075412, A075415, A178630, A178631, A178632, A178633, A178634.
%Y A178635 Cf. A002275, A002282, A002283, A002477.
%K A178635 nonn,easy
%O A178635 1,1
%A A178635 _Reinhard Zumkeller_, May 31 2010