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A272068 a(n) = (10^n-1)^5.

%I A272068 #34 Mar 30 2025 10:34:28
%S A272068 0,59049,9509900499,995009990004999,99950009999000049999,
%T A272068 9999500009999900000499999,999995000009999990000004999999,
%U A272068 99999950000009999999000000049999999,9999999500000009999999900000000499999999,999999995000000009999999990000000004999999999,99999999950000000009999999999000000000049999999999
%N A272068 a(n) = (10^n-1)^5.
%C A272068 The sum of the digits of a(n) is divisible by 27. For example, 9^5 = 59049 and 5 + 9 + 0 + 4 + 9 = 27 * 1.
%C A272068 Number of 9 in a(n) is 3*n-1 for n > 0. - _Seiichi Manyama_, Sep 18 2018
%H A272068 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (111111,-1122322110,1123333211000,-112232211000000,1111110000000000,-1000000000000000).
%F A272068 a(n) = A002283(n)^5.
%F A272068 From _Ilya Gutkovskiy_, Apr 19 2016: (Start)
%F A272068 O.g.f.: 59049*x*(1 + 49940*x + 78366000*x^2 + 4994000000*x^3 + 10000000000*x^4)/((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)*(1 - 10000*x)*(1 - 100000*x)).
%F A272068 E.g.f.: -exp(x) + 5*exp(10*x) - 10*exp(100*x) + 10*exp(1000*x) - 5*exp(10000*x) + exp(100000*x). (End)
%e A272068 From _Seiichi Manyama_, Sep 18 2018: (Start)
%e A272068 n| a(n) can be divided into 5 parts for n > 1.
%e A272068 -+--------------------------------------------
%e A272068 1|        5    9    04    9
%e A272068 2|   9   50   99   004   99
%e A272068 3|  99  500  999  0004  999
%e A272068 4| 999 5000 9999 00004 9999
%e A272068 (End)
%p A272068 A272068:=n->(10^n-1)^5: seq(A272068(n), n=0..10); # _Wesley Ivan Hurt_, Apr 19 2016
%t A272068 (10^Range[0, 10] - 1)^5 (* _Wesley Ivan Hurt_, Apr 19 2016 *)
%o A272068 (Ruby)
%o A272068 (0..n).each{|i| p ('9' * i).to_i ** 5}
%o A272068 (PARI) a(n) = (10^n-1)^5; \\ _Michel Marcus_, Apr 19 2016
%o A272068 (Magma) [(10^n-1)^5 : n in [0..10]]; // _Wesley Ivan Hurt_, Apr 19 2016
%Y A272068 Cf. A002283, A059988, A272066, A272067, A319358.
%K A272068 nonn,easy
%O A272068 0,2
%A A272068 _Seiichi Manyama_, Apr 19 2016