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%I #19 Nov 16 2016 12:37:23
%S 0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,
%T 9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,
%U 0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9,9,0,0,9
%N Decimal expansion of 1/101.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1).
%F From _Wesley Ivan Hurt_, Jun 04 2016: (Start)
%F G.f.: 9*x^2/(1-x)*(1+x^2).
%F a(n) = a(n-1) - a(n-2) + a(n-3) for n>2.
%F a(n) = 9*(1+(-1)^((2*n+3+(-1)^n)/4))/2 = 9*A133872(n+2).
%F a(n) = 9*(1+i)*(1-i-i^(-n)+i^(1+n))/4 where i=sqrt(-1).
%F a(2k) = A010680(k), a(2k+1) = A010680(k+1). (End)
%F E.g.f.: 9*(-sin(x) - cos(x) + sinh(x) + cosh(x))/2. - _Ilya Gutkovskiy_, Jun 04 2016
%p Digits:=100: evalf(1/101); # _Wesley Ivan Hurt_, Jun 04 2016
%t Flatten[RealDigits[1/101, 10, 100, -1]] (* _Wesley Ivan Hurt_, Jun 04 2016 *)
%o (PARI) a(n) = {r=lift(Mod(10,101)^(n-1));floor(10*r/101)} \\ _Michael B. Porter_, Oct 01 2009
%Y Cf. A010680, A133872.
%K nonn,cons,easy
%O 0,3
%A _N. J. A. Sloane_
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