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%I #46 Feb 06 2024 11:58:51
%S 0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,
%T 0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,
%U 0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9,0,9
%N Decimal expansion of 1/11.
%C Period 2: repeat [0,9].
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F a(n) = (9/2)*(1 - (-1)^n) = 9*(n mod 2). - _Paolo P. Lava_, Oct 31 2006
%F From _Elmo R. Oliveira_, Jan 15 2024: (Start)
%F a(n) = a(n-2) for n >= 2.
%F a(n) = 3 * A010674(n).
%F G.f.: 9*x/(1-x^2).
%F E.g.f.: 9*sinh(x). (End)
%F a(n) = 9 * A000035(n). - _Alois P. Heinz_, Jan 16 2024
%e 1/11 = 0.0909090909090909090909090909090909090909090909090909090909...
%t RealDigits[1/11, 10, 100][[1]] (* _Alonso del Arte_, Mar 11 2018 *)
%o (PARI) a(n) = 9*(n%2); \\ _Altug Alkan_, Mar 25 2018
%Y Cf. A000035, A010674.
%Y Bisections give: A000004, A010734.
%K nonn,easy,cons
%O 0,2
%A _N. J. A. Sloane_
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