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%I #23 Sep 08 2022 08:45:54
%S 45,5445,554445,55544445,5555444445,555554444445,55555544444445,
%T 5555555444444445,555555554444444445,55555555544444444445,
%U 5555555555444444444445,555555555554444444444445
%N a(n) = 45 * ((10^n - 1)/9)^2.
%H Vincenzo Librandi, <a href="/A178632/b178632.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) = 45*A002477(n) = A002283(n)*A002279(n).
%F a(n) = (A002279(n-1)*10^n + A002278(n))*10 + 5.
%F G.f.: 45*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - _Ilya Gutkovskiy_, Feb 24 2017
%e n=1: ..................... 45 = 9 * 5;
%e n=2: ................... 5445 = 99 * 55;
%e n=3: ................. 554445 = 999 * 555;
%e n=4: ............... 55544445 = 9999 * 5555;
%e n=5: ............. 5555444445 = 99999 * 55555;
%e n=6: ........... 555554444445 = 999999 * 555555;
%e n=7: ......... 55555544444445 = 9999999 * 5555555;
%e n=8: ....... 5555555444444445 = 99999999 * 55555555;
%e n=9: ..... 555555554444444445 = 999999999 * 555555555.
%t 45 (FromDigits/@Table[PadRight[{}, n, 1], {n, 20}])^2 (* _Vincenzo Librandi_, Mar 20 2014 *)
%t LinearRecurrence[{111,-1110,1000},{45,5445,554445},20] (* _Harvey P. Dale_, Jan 23 2019 *)
%o (Magma) [45*((10^n-1)/9)^2: n in [1..50]]; // _Vincenzo Librandi_, Dec 28 2010
%o (Maxima) A178632(n):=45*((10^n-1)/9)^2$ makelist(A178632(n),n,1,12); /* _Martin Ettl_, Nov 08 2012 */
%o (PARI) a(n)=45*(10^n\9)^2 \\ _Charles R Greathouse IV_, Jul 02 2013
%Y Cf. A075412, A178630, A178631, A075415, A178633, A178634, A178635, A059988.
%K nonn,easy
%O 1,1
%A _Reinhard Zumkeller_, May 31 2010
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