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A019430
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Continued fraction for tan(1/7).
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4
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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, 173, 1, 187, 1, 201, 1, 215, 1, 229, 1, 243, 1, 257, 1, 271, 1, 285, 1, 299, 1, 313, 1, 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
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (-1+3*(-1)^n-7*(-1+(-1)^n)*n)/2 for n>1.
a(n) = 2*a(n-2)-a(n-4) for n>5.
G.f.: x*(x^4-x^3+7*x^2+x+6) / ((x-1)^2*(x+1)^2). (End)
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EXAMPLE
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0.14383695943619093528003059... = 0 + 1/(6 + 1/(1 + 1/(19 + 1/(1 + ...)))). - Harry J. Smith, Jun 14 2009
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MATHEMATICA
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Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Tan[1/7], 80]] (* Harvey P. Dale, Feb 01 2013 *)
Join[{0, 6}, LinearRecurrence[{0, 2, 0, -1}, {1, 19, 1, 33}, 100]] (* Vincenzo Librandi, Jan 03 2016 *)
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PROG
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(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
(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
(Magma) [0, 6] cat [(-1+3*(-1)^n-7*(-1+(-1)^n)*n)/2: n in [2..80]]; // Vincenzo Librandi, Jan 03 2016
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CROSSREFS
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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STATUS
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approved
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