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A019430 Continued fraction for tan(1/7).

%I A019430 #30 Oct 03 2023 08:59:13
%S A019430 0,6,1,19,1,33,1,47,1,61,1,75,1,89,1,103,1,117,1,131,1,145,1,159,1,
%T A019430 173,1,187,1,201,1,215,1,229,1,243,1,257,1,271,1,285,1,299,1,313,1,
%U A019430 327,1,341,1,355,1,369,1,383,1,397,1,411,1,425,1,439,1,453,1,467,1,481,1,495,1,509,1
%N A019430 Continued fraction for tan(1/7).
%H A019430 Harry J. Smith, <a href="/A019430/b019430.txt">Table of n, a(n) for n = 0..20000</a>
%H A019430 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A019430 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A019430 From _Colin Barker_, Sep 08 2013: (Start)
%F A019430 a(n) = (-1+3*(-1)^n-7*(-1+(-1)^n)*n)/2 for n>1.
%F A019430 a(n) = 2*a(n-2)-a(n-4) for n>5.
%F A019430 G.f.: x*(x^4-x^3+7*x^2+x+6) / ((x-1)^2*(x+1)^2). (End)
%e A019430 0.14383695943619093528003059... = 0 + 1/(6 + 1/(1 + 1/(19 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 14 2009
%t A019430 Block[{$MaxExtraPrecision=1000},ContinuedFraction[Tan[1/7],80]] (* _Harvey P. Dale_, Feb 01 2013 *)
%t A019430 Join[{0, 6}, LinearRecurrence[{0, 2, 0, -1}, {1, 19, 1, 33}, 100]] (* _Vincenzo Librandi_, Jan 03 2016 *)
%o A019430 (PARI) { allocatemem(932245000); default(realprecision, 96000); x=contfrac(tan(1/7)); for (n=0, 20000, write("b019430.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 14 2009
%o A019430 (PARI) Vec(x*(x^4-x^3+7*x^2+x+6)/((x-1)^2*(x+1)^2) + O(x^100)) \\ _Colin Barker_, Sep 08 2013
%o A019430 (Magma) [0, 6] cat [(-1+3*(-1)^n-7*(-1+(-1)^n)*n)/2: n in [2..80]]; // _Vincenzo Librandi_, Jan 03 2016
%Y A019430 Cf. A161016 (decimal expansion), A019425 through A019433.
%K A019430 nonn,cofr,easy
%O A019430 0,2
%A A019430 _David W. Wilson_