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%I #22 Sep 08 2022 08:46:16
%S 0,6561,96059601,996005996001,9996000599960001,99996000059999600001,
%T 999996000005999996000001,9999996000000599999960000001,
%U 99999996000000059999999600000001,999999996000000005999999996000000001,9999999996000000000599999999960000000001,99999999996000000000059999999999600000000001
%N a(n) = (10^n-1)^4.
%C 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 Number of 9 in a(n) is 2*n-2 for n > 0. - _Seiichi Manyama_, Sep 18 2018
%F a(n) = A059988(n)^2 = A002283(n)^4.
%F From _Ilya Gutkovskiy_, Apr 19 2016: (Start)
%F 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 E.g.f.: (1 - 4*exp(9*x) + 6*exp(99*x) - 4*exp(999*x) + exp(9999*x))*exp(x). (End)
%e From _Seiichi Manyama_, Sep 18 2018: (Start)
%e n| a(n) can be divided into 4 parts for n > 1.
%e -+--------------------------------------------
%e 1| 65 61
%e 2| 9 605 9 601
%e 3| 99 6005 99 6001
%e 4| 999 60005 999 60001
%e (End)
%p A272067:=n->(10^n-1)^4: seq(A272067(n), n=0..15); # _Wesley Ivan Hurt_, Apr 19 2016
%t (10^Range[0, 10] - 1)^4 (* _Wesley Ivan Hurt_, Apr 19 2016 *)
%o (Ruby)
%o (0..n).each{|i| p ('9' * i).to_i ** 4}
%o (PARI) a(n) = (10^n-1)^4; \\ _Michel Marcus_, Apr 19 2016
%o (Magma) [(10^n-1)^4 : n in [0..10]]; // _Wesley Ivan Hurt_, Apr 19 2016
%Y Cf. A002283, A059988, A272066, A272068, A319358.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Apr 19 2016
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