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%I #22 Jan 17 2024 01:34:21
%S 29,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,
%T 3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,
%U 58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1,58,1,3,1
%N Continued fraction for sqrt(888).
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F From _Wesley Ivan Hurt_, Aug 29 2015: (Start)
%F G.f.: (29+x+3*x^2+x^3+29*x^4)/(1-x^4).
%F a(n) = 2+(-1)^n+55*((1+(-1)^(n/2))*(1+(-1)^n))/4, n>0. (End)
%F From _Amiram Eldar_, Jan 17 2024: (Start)
%F Multiplicative with a(2) = 3, a(2^e) = 58 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) + 55/2^(2*s)). (End)
%p with(numtheory): Digits := 300: convert(evalf(sqrt(888)),confrac);
%t CoefficientList[Series[(29 + x + 3 x^2 + x^3 + 29 x^4)/(1 - x^4), {x, 0, 30}], x] (* or *) Join[{29}, Table[2 + (-1)^n + 55 ((1 + (-1)^(n/2))*(1 + (-1)^n))/4, {n, 100}]] (* _Wesley Ivan Hurt_, Aug 29 2015 *)
%t ContinuedFraction[Sqrt[888], 100] (* _Amiram Eldar_, Jan 17 2024 *)
%K nonn,cofr,easy,mult
%O 0,1
%A _N. J. A. Sloane_
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