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A272067 a(n) = (10^n-1)^4.

%I A272067 #24 Mar 30 2025 10:31:00
%S A272067 0,6561,96059601,996005996001,9996000599960001,99996000059999600001,
%T A272067 999996000005999996000001,9999996000000599999960000001,
%U A272067 99999996000000059999999600000001,999999996000000005999999996000000001,9999999996000000000599999999960000000001,99999999996000000000059999999999600000000001
%N A272067 a(n) = (10^n-1)^4.
%C A272067 The sum of the digits of a(n) is divisible by 18. For example, 9^4 = 6561 and 6 + 5 + 6 + 1 = 18 * 1.
%C A272067 Number of 9 in a(n) is 2*n-2 for n > 0. - _Seiichi Manyama_, Sep 18 2018
%H A272067 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (11111,-11222110,1122211000,-11111000000,10000000000).
%F A272067 a(n) = A059988(n)^2 = A002283(n)^4.
%F A272067 From _Ilya Gutkovskiy_, Apr 19 2016: (Start)
%F A272067 O.g.f.: 6561*x*(1 + 100*x)*(1 + 3430*x + 10000*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)*(1 - 10000*x)).
%F A272067 E.g.f.: (1 - 4*exp(9*x) + 6*exp(99*x) - 4*exp(999*x) + exp(9999*x))*exp(x). (End)
%e A272067 From _Seiichi Manyama_, Sep 18 2018: (Start)
%e A272067 n| a(n) can be divided into 4 parts for n > 1.
%e A272067 -+--------------------------------------------
%e A272067 1|        65        61
%e A272067 2|   9   605   9   601
%e A272067 3|  99  6005  99  6001
%e A272067 4| 999 60005 999 60001
%e A272067 (End)
%p A272067 A272067:=n->(10^n-1)^4: seq(A272067(n), n=0..15); # _Wesley Ivan Hurt_, Apr 19 2016
%t A272067 (10^Range[0, 10] - 1)^4 (* _Wesley Ivan Hurt_, Apr 19 2016 *)
%o A272067 (Ruby)
%o A272067 (0..n).each{|i| p ('9' * i).to_i ** 4}
%o A272067 (PARI) a(n) = (10^n-1)^4; \\ _Michel Marcus_, Apr 19 2016
%o A272067 (Magma) [(10^n-1)^4 : n in [0..10]]; // _Wesley Ivan Hurt_, Apr 19 2016
%Y A272067 Cf. A002283, A059988, A272066, A272068, A319358.
%K A272067 nonn,easy
%O A272067 0,2
%A A272067 _Seiichi Manyama_, Apr 19 2016